answer with explanation Answer: Option D Explanation: Let the numbers be $2x$ and $3x$LCM of $2x$ and $3x$ $=6x~~$ (∵ LCM of 2 and 3 is 6. Hence LCM of $2x$ and $3x$ is $6x$)Given that LCM of $2x$ and $3x$ is 48=> $6x=48$=> $x=\dfrac{48}{6}=8$Sum of the numbers$=2x+3x\\=5x$ = 5 × 8 = 40
answer with explanation Answer: Option B Explanation: Greatest number of four digits = 9999LCM of 15, 25, 40 and 75 = 6009999 ÷ 600 = 16, remainder = 399Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75 = 9999 - 399 = 9600
answer with explanation Answer: Option B Explanation: Let the numbers be $2x$, $3x$ and $4x$LCM of $2x$, $3x$ and $4x$ = $12x$$12x=240\\~\\\Rightarrow x=\dfrac{240}{12}=20$ H.C.F of $2x$, $3x$ and $4x$ $=x=20$
answer with explanation Answer: Option D Explanation:  LCM = 2 × 2 × 3 × 1 × 3 × 5 = 180
answer with explanation Answer: Option A Explanation: Solution 1LCM of 5, 6, 7 and 8 = 840Hence the number can be written in the form (840k + 3) which is divisible by 9.If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9.If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9. Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder. Solution 2 - Hit and Trial MethodJust see which of the given choices satisfy the given condtions.Take 3363. This is not even divisible by 9. Hence this is not the answer.Take 1108. This is not even divisible by 9. Hence this is not the answer.Take 2007. This is divisible by 9.2007 ÷ 5 = 401, remainder = 2 . Hence this is not the answerTake 1683. This is divisible by 9.1683 ÷ 5 = 336, remainder = 31683 ÷ 6 = 280, remainder = 31683 ÷ 7 = 240, remainder = 31683 ÷ 8 = 210, remainder = 3 Hence 1683 is the answer Set 1Set 2Set 3Set 4Set 5Set 6
How to find out sum of numbers if their lcm given..? The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is? The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is?Since h.c.f. is 13, these numbers can be written as 13a and 13b.Now, according to the question, we have product of these numbers is 2028.Then, 13a × 13b = 2028.=> a × b=12Prime factors of 12 are 2,3.12 = 2×2×3.Number of factors of 12 =(2+1)(1+1)=6Since 12 is not a perfect Square, so we can express 12 in $\frac{6}{2}$ = 3 ways as a product of two numbers. Hence, Required no. of pairs = 3 Ans. Since h.c.f. is 13, these numbers can be written as 13a and 13b.Now, according to the question, we have product of these numbers is 2028.Then, 13a × 13b = 2028.=> a × b=12Prime factors of 12 are 2,3.12 = 2×2×3.Number of factors of 12 =(2+1)(1+1)=6Since 12 is not a perfect Square, so we can express 12 in $\frac{6}{2}$ = 3 ways as a product of two numbers.<p>Hence, Required no. of pairs = 3 Ans.</p>Going by your argument, the 3 ways of expressing 12 as product of two number are12 = 1×1212 = 2×612 = 3×4In this, you can not take 2,6 because they are not co-prime. Suppose we take (2,6) thennumbers are 26, 78But HCF(26,78) is not 13.Generally, you can only take such pairs which are co-prime (1,12) and (3,4) are fine and as explained by Jay, answer is 2 Going by your argument, the 3 ways of expressing 12 as product of two number are12 = 1×1212 = 2×612 = 3×4In this, you can not take 2,6 because they are not co-prime. Suppose we take (2,6) thennumbers are 26, 78But HCF(26,78) is not 13.Generally, you can only take such pairs which are co-prime<p>(1,12) and (3,4) are fine and as explained by Jay, answer is 2</p>Take numbers as 13a and 13b (because 13 is the HCF)13a * 13b = 2028ab = 1212 can be written as a product of co-prime numbers in the following waysa. 1*12b. 3*4(i.e., two ways)So required number of ways = 2 The pairs are (13*1, 13*12) and (13*3, 13*4) Take numbers as 13a and 13b (because 13 is the HCF)13a * 13b = 2028ab = 1212 can be written as a product of co-prime numbers in the following waysa. 1*12b. 3*4(i.e., two ways)So required number of ways = 2<p>The pairs are (13*1, 13*12) and (13*3, 13*4)</p>If LCM of 15,20,X=180 then what is the value of X??? If LCM of 15,20,X=180 then what is the value of X???Many values are possible.15 = 3*520 = 2*2*5LCM of 15 and 20 = 3*2*2*5=60(3*2*2*5) * 3 = 180ie, an additional 3 should be there to make the LCM 180 number can be 3*3=9, 3*5*3=45, 2*2*5*3*3 = 180, etc Many values are possible.15 = 3*520 = 2*2*5LCM of 15 and 20 = 3*2*2*5=60(3*2*2*5) * 3 = 180ie, an additional 3 should be there to make the LCM 180<p>number can be 3*3=9, 3*5*3=45, 2*2*5*3*3 = 180, etc</p>the HCF of 2 number is 98 and their LCM is 2352.the sum of the number may be a.1372 b.1398 c.1426 d.1484 the HCF of 2 number is 98 and their LCM is 2352.the sum of the number may be<p>a.1372</p><p>b.1398</p><p>c.1426</p><p>d.1484</p>X*y= 98*2352 X*y=98*98*12*2 X*y= (98*2)*(98*12) As compair to x and y then X= 98*2 X= 196 Y = 98*12 Y= 1176 Then X+y 196+1176= 1372 X*y= 98*2352<p>X*y=98*98*12*2</p><p>X*y= (98*2)*(98*12)</p><p>As compair to x and y then </p><p>X= 98*2</p><p>X= 196</p><p>Y = 98*12</p><p>Y= 1176</p><p>Then</p><p>X+y</p><p>196+1176= 1372</p>In the question, 'none of these' is not given as an option and 1372 is the only number divisible by 98. So one can directly write the answer as 1372 In the question, 'none of these' is not given as an option and 1372 is the only number divisible by 98. So one can directly write the answer as 13721234 ... 6Next1-10 of 60 comments
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Q.1 The LCM of two numbers is 864 and their HCF is 144. If one of the number is 288, the other number is : 576 1296 432 144
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Q.2 LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number will be: 5 25 45 225
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Q.3 The L.C.M. of two numbers is 1820 and their H.C.F. is 26. If one number is 130 then the other number is : 70 1690 364 1264
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Q.4 The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number 204 240 260 320
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Q.5 The HCF of two numbers 12906 and 14818 is 478. Their LCM is 400086 200043 600129 800172
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Q.6 The H.C.F. and L.C.M. of two 2- digit numbers are 16 and 480 re- spectively. The numbers are 40, 48 60, 72 64, 80 80, 96
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Q.7 The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is 48 80 96 112
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Q.8 The product of two numbers is 4107. If the H.C.F. of the numbers is 37, the greater number is 185 111 107 101
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Q.9 The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60, the other is 50 75 65 100
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Q.10 The HCF and LCM of two num- bers are 12 and 924 respectively. Then the number of such pairs i 0 1 2 3
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Q.11 The LCM of two numbers is 30 and their HCF is 5. One of the number is 10. The other is 20 25 15 5
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Q.12 The product of two numbers is 1280 and their H.C.F. is 8. The L.C.M. of the number will be 160 150 120 140
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Q.13 The H.C.F. and L.C.M. of two numbers are 8 and 48 respec- tively. If one of the number is 24, then the other number is 48 36 24 16
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Q.14 The H.C.F and L.C.M of two num- bers are 12 and 336 respectively. If one of the number is 84, the other is 36 48 72 96
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Q.15 The product of two numbers is 216. If the HCF is 6, then their LCM is 72 60 48 36
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Q.16 The HCF and LCM of two num- bers are 18 and 378 respectively. If one of the number is 54, then the other number is 126 144 198 238
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Q.17 The HCF and product of two numbers are 15 and 6300 re- spectively. The number of possi- ble pairs of the numbers is 4 3 2 1
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Q.18 The HCF of two numbers is 15 and their LCM is 225. If one of the number is 75, then the other number is 105 90 60 45
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Q.19 The LCM of two numbers is 520 and their HCF is 4. If one of the number is 52, then the other number is 40 42 50 52
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Q.20 The H.C.F. of two numbers is 96 and their L.C.M. is 1296. If one of the number i s 864, the other is 132 135 140 144
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Q.21 The LCM of two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the number is 100, then the other number is 5 25 100 125
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Q.22 Product of two co-prime numbers is 117. Then their L.C.M. is 117 9 13 39
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Q.23 The product of two numbers is 2160 and their HCF is 12. Num- ber of such possible pairs is 1 2 3 4
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Q.24 LCM of two numbers is 2079 and their HCF is 27. If one of the number is 189, the other num- ber is 297 584 189 216
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Q.25 The product of two numbers is 2028 and their HCF is 13. The number of such pairs is 1 2 3 4
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Q.26 The HCF and LCM of two num- bers are 13 and 455 respectively. If one of the number lies between 75 and 125, then, that number is : 78 91 104 117
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Q.27 The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.? 24 48 56 60
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Q.28 The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of the two numbers is : 276 299 345 322
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Q.29 The L.C.M. of three different num- bers is 120. Which of the follow- ing cannot be their H.C.F.? 8 12 24 35
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Q.30 The H.C.F. and L.C.M. of two numbers are 44 and 264 respec- tively. If the first number is di- vided by 2, the quotient is 44. The other number is 147 528 132 264
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Q.31 The least number which when divided by 4, 6, 8, 12 and 16 leaves a remainder of 2 in each case is 46 48 50 56
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Q.32 The least number, which when divided by 12, 15, 20 or 54 leaves a remainder of 4 in each case, is 450 454 540 544
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Q.33 Find the greatest number of five digits which when divided by 3, 5, 8, 12 have 2 as remainder 99999 99958 99960 99962
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Q.34 The least multiple of 13, which on dividing by 4, 5, 6, 7 and 8 leaves remainder 2 in each case is 2520 842 2522 840
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Q.35 A, B, C start running at the same time and at the same point in the same direction in a circular sta- dium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds. After what time will they meet again at the start- ing point ? 26 minutes 18 seconds 42 minutes 36 seconds 45 minutes 46 minutes 12 seconds
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Q.36 Find the largest number of four digits such that on dividing by 15, 18, 21 and 24 the remainders are 11, 14, 17 and 20 respectively. 6557 7556 5675 7664
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Q.37 The least perfect square, which is divisible by each of 21, 36 and 66 is 214344 214434 213444 231444
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Q.38 The least number, which when divided by 4, 5 and 6 leaves re- mainder 1, 2 and 3 respectively, is 57 59 61 63
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Q.39 Let the least number of six dig- its which when divided by 4, 6, 10, 15 leaves in each case same remainder 2 be N. The sum of digits in N is : 3 5 4 6
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Q.40 Which is the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ? 2520 1260 630 196
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Q.41 The smallest square number di- visible by 10, 16 and 24 is 900 1600 2500 3600
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Q.42 If the students of a class can be grouped exactly into 6 or 8 or 10, then the minimum number of students in the class must be 60 120 180 240
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Q.43 The least number which when divided by 4, 6, 8 and 9 leave zero remainder in each case and when divided by 13 leaves a re- mainder of 7 is : 144 72 36 85
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Q.44 The smallest number, which when divided by 12 and 16 leaves remainder 5 and 9 respec- tively, is : 55 41 39 29
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Q.45 A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7, is : 1539 539 359 1359
Ans . 3 Using Rule Number 5,
Q.46 What is the smallest number which leaves remainder 3 when divided by any of the numbers 5, 6 or 8 but leaves no remain- der when it is divided by 9 ? 123 603 723 243
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Q.47 The least number which when di- vided by 16, 18, 20 and 25 leaves 4 as remainder in each case but when divided by 7 leaves no re- mainder is 17004 18000 18002 18004
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Q.48 What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but when di- vided by 13 leaves no remainder ? 312 962 1562 1586
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Q.49 The least multiple of 7, which leaves the remainder 4, when divided by any of 6, 9, 15 and 18, is 76 94 184 364
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Q.50 The largest number of five digits which, when divided by 16, 24, 30, or 36 leaves the same re- mainder 10 in each case, is 99279 99370 99269 99350
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Q.51 The smallest number, which when divided by 5, 10, 12 and 15, leaves remainder 2 in each case; but when divided by 7 leaves no remainder, is 189 182 175 91
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Q.52 What least number must be sub- tracted from 1936 so that the resulting number when divided by 9, 10 and 15 will leave in each case the same remainder 7 ? 37 36 39 30
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Q.53 The least number, which when divided by 18, 27 and 36 sepa- rately leaves remainders 5,14, and 23 respectively, is 95 113 149 77
Ans . 1
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The LCM of two numbers is 2028 and their HCF is 25 if one of the number is 100 find the other
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