What is the smallest number which when divided by 24 36 and 54 gives 5 as remainder each time?

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What is the smallest number which when divided by 24, 36 and 54 gives a remainder of 5 each time?

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What is the smallest number which when divided by 24 36 and 54 gives 5 as remainder each time?

Question

What is the smallest number which when divided by 24,36 and 54 gives a remainder of 5 each time?

Hard Open in App Solution Verified by Toppr Let's factorize, 24 = 2x2x2x3 36 = 2x2x3x3 54 = 2x3x3x3

The smallest number divisible by all 24, 36, 54 is:

LCM(24, 36, 54) = 216

Thus, to get 5 as remainder, we need to add 5 to 216.

(as 216 is the smallest number which gives remainder 0 when divided by 24 or 36 or 54)

216 + 5 = 221

For 12, 221 gives 18 as quotient and 5 as remainder

For 36, 221 gives 6 as quotient and 5 as remainder

For 54, 221 gives 4 as quotient and 5 as remainder

Hence, 221 is required number.

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[Solved] Find the smallest number which when divided by 48 and 60, le

Given∶ A number when divided by 48 and 60, leaves a remainder 7 in each case. But when divided by 13 leaves no remainder. Formula Used∶ Concept of LCM a

What is the smallest number which when divided by 24 36 and 54 gives 5 as remainder each time?

Home Quantitative Aptitude Number System LCM and HCF LCM

Question

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Find the smallest number which when divided by 48 and 60, leaves a remainder 7 in each case but when divided by 13 leaves no remainder. Find the sum of the digits in this required smallest number.

13 14 15 11

Answer (Detailed Solution Below)

Option 1 : 13

What is the smallest number which when divided by 24 36 and 54 gives 5 as remainder each time?

Detailed Solution

Download Solution PDF

Given

A number when divided by 48 and 60, leaves a remainder 7 in each case.

But when divided by 13 leaves no remainder.

Formula Used

Concept of LCM and Hit and Trial method

Calculation

LCM of 48 and 60 = 24 × 3 × 5 = 240

Let the required number be N

So, N = 240 × x + 7

Now use Hit and Trial method

When, x = 1

Then, N = 240 × 1 + 7 = 240 + 7 = 247

Hence, sum of the digits = 2 + 4 + 7 = 13

∴ 13 is the sum of the digits in the required smallest number which when divided by 48 and 60 leaves a remainder 7, but when divided by 13, the remainder is zero.

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स्रोत : testbook.com

What is the smallest natural number which when divided by 24, 18, 40 and 60 leave remainder 8 in each case?

Answer (1 of 6): LCM is the least no. /Smallest no. Which is divisible by all the given numbers. So, LCM of 24= 2× 2×2×3, 18= 2×3×3, 40= 2×2×2×5, 60=2×2×3×5, is all factors with greatest power, so LCM = 2^3 ×3^2 ×5^1= 8×9× 5 = 360. So , no. Leaves remainder 8 in each case is 360+8 = 368.

What is the smallest number which when divided by 24 36 and 54 gives 5 as remainder each time?

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What is the smallest natural number which when divided by 24, 18, 40 and 60 leave remainder 8 in each case?

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6 Answers HsBadarinath

Ph.D. in Civil Engineering. Maths keeps one mentally active.Upvoted by

Krogi Us

, M.Sc. Mathematics & Computer Science, Aalto University (1988)Author has 52.3K answers and 32.9M answer viewsUpdated 4y

Factors of 24 = 2x2x2x3 18 = 2x3x3 40 = 2x2x2x5 60 = 2x2x3x5

LCM = 2x2x2x3x3x5 = 360

360+8 = 368. Answer is 368. Related questions

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Ali Dursen

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Michael Jørgensen

, PhD in mathematicsAuthor has 220 answers and 135.7K answer views4y

Such a number would be 8 greater than a number that is divisible by all those numbers. Since we want the smallest, answer is 0+8.

TARUN SHARMA

Works at MathematicsUpvoted by

Krogi Us

, M.Sc. Mathematics & Computer Science, Aalto University (1988)4y

LCM is the least no. /Smallest no. Which is divisible by all the given numbers. So, LCM of 24= 2× 2×2×3, 18= 2×3×3, 40= 2×2×2×5, 60=2×2×3×5, is all factors with greatest power, so LCM = 2^3 ×3^2 ×5^1= 8×9× 5 = 360. So , no. Leaves remainder 8 in each case is 360+8 = 368.

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prime factors of 24,18,40 and 60 are:

24=2^3*3 18=2*3^2 40=2^3*5 60=2^2*3*5

Thus L;CM (24,18,40,60)=2^3 *3^2*5

=8*9*5=360

THE REMAINDER IN ALL CASES IS 8

HENCE THE NUMBER=LCM+8=368

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24= 2 3 ×318=2× 3 2 40= 2 3 ×560= 2 2 ×3×5

24=23×318=2×3240=23×560=22×3×5

L.C.M. (24, 18, 40, 60) =

2 3 × 3 2 ×5=360

L.C.M. (24, 18, 40, 60) =23×32×5=360

⟹360 + 8 = 368 is the smallest number which when divided by

⟹360 + 8 = 368 is the smallest number which when divided by

24, 18, 40 and 60 leave remainder 8 in each case.

24, 18, 40 and 60 leave remainder 8 in each case.

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