The product of hcf and lcm of two numbers is 60 and one number is 4 then find the other number

Also Read Similar Questions Below :

⇒ A father is twice as old as his son. 20 years ago the age of the father was 12 times the age of the son. The present age of the father is :44 years32 years22 years

45 years

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HCF and LCM Relation
HCF and LCM of Positve Integers
HCF and LCM of Co-Prime numbers
HCF and LCM of Fractions
Relation between HCF and LCM of 3 Numbers
Related Articles on Relation Between HCF and LCM
FAQs on Relation Between HCF and LCM
What is LCM of Two Numbers?
What is the Highest Common Factor?
What is the Relation Between HCF and LCM of co-prime numbers?
What are H.C.F. and L.C.M. of Fractions?
What is the Difference Between LCM and HCF?

⇒ The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:504536544

548

⇒ HCF of three numbers is 12. If they are in the ratio 1:2:3, then the numbers are------------12,24,3610,20,305,10,15

4,8,12

⇒

The HCF and LCM of two numbers are 44 and 264 respectively. If the first number is divisible by 3, then the first number is

264132both a and b

⇒ Three numbers are in the ratio 2:3:5 and their H.C.F. is 8. The numbers are32,48,808,12,2012,18,30

16,24,40

⇒ The LCM and HCF of two numbers is 48 and 8. If one of the numbers is 16, find the other number.241232

⇒ Five bells commence tolling together and toll at intervals of 2, 5, 6, 8 and 9 seconds respectively. How many times do they toll together in an hour?111210

⇒ The HCF and LCM of two numbers is 2 and 70. If the sum of the numbers is 24, find the smallest of the two numbers.14107

⇒ Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is456

⇒ What least number must be subtracted from 1294 so that the remainder when divided 9, 11, 13 will leave in each case the same remainder 6 ?412

⇒ The ratio of Vimal's age and Aruna's age is 3:5 and sum of their ages is 80 years. The ratio of their ages after 10 years will be :-2:31:23:2

3:5

⇒ The HCF of two numbers is 16 and their LCM is 160. If one of the numbers is 32, then the other number is ---488096

112

⇒ The G.C.D. of 1.08, 0.36 and 0.9 is:0.030.90.18

0.108

⇒ The ages of Ravi Rani are in the ratio of 3:5. After 9 years, the ratio of their ages will become 3:4. The present age of Rani is : (in years )91518

⇒ The HCF of two numbers is 12 and their difference is also 12. The numbers are------------66,7894,10670,82

84,96

⇒ The traffic lights at three different road crossing change after every 48 sec; 72 sec; and 108 sec., respectively. If they all change simultaneously at 8:20:00 hrs, then they will again change simultaneously at8:27:12 Hrs8:27:24 Hrs8:27:36 Hrs

8:27:48 Hrs

⇒ The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:101107111

185

⇒ Find the LCM of the first seven natural numbers.16884840

420

⇒ LCM of 87 and 145 is :-----------8701305435

1740

⇒ The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the numbers is 77, find the other.668979

⇒ Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.479

⇒ The ratio of the ages of Jaya and Ravi is 2:5. After 8 years, their ages will be in the ratio of 1:2. The difference in their present ages is : ( in years )243629

⇒ The L.C.M. of two numbers is 48. The numbers are in the ratio 2: 3. The sum of the numbers is :283240

⇒ The traffic signals at four road crossings change every 30 seconds, 1 minute, 45 seconds and 75 seconds respectively. If they changed simultaneously at 9:00 am, at what time will they change simultaneously again?9:12 am9:15 am9:20 am

9:30 am

⇒ Harshini has three pieces of thread of length 15m, 18m and 24m. She is asked to cut them into smaller pieces of equal length such that no piece of thread gets wasted. Find the minimum number of smaller threads she will get.197224

⇒ One year ago Jaya was four times as old as her daughter Nikitha. Six years hence, Mrs.Jaya's age will exceed her daughter's age by 9 years. The ratio of the present ages of Jaya and her daughter is :9 : 211: 312: 5

13: 4

⇒ Find the lowest common multiple of 24, 36 and 40.120240360

480

⇒ The H.C.F. of two numbers is 19 and their L.C.M. is 114. If one of the numbers is 57, find the other number.22811495

⇒ The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is233313

⇒ Jayesh is as much younger to Anil as he is older to Prashant. If the sum of the ages of Anil and Prashant is 48 years, what is the age of Jayesh?23 years24 years35 years

25 years

HCF and LCM are the two terms that stand for highest common factor and least common multiple respectively. The HCF is the greatest factor of two numbers or more than two numbers which divides the number exactly with no remainder, while on the contrary the LCM of two numbers or more than two numbers is the smallest number which is divisible by given numbers exactly. After discussing the definition of HCF and LCM, in this article, we will focus on the relation between HCF and LCM along with solved examples and practice questions.

HCF and LCM Relation

The multiplication of common prime factors of given numbers with the least exponential powers is the HCF of two numbers or more numbers. For example, The HCF of 12 and 20 is 4. Prime factors of 12 = 2 × 2× 3 Prime factors of 20 = 2 × 2 ×5 HCF is 2 × 2=4

The LCM or the least common multiple is the smallest natural number which is a multiple of two or more numbers. For example, the LCM of 12 and 20 is 60.

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84 and so on. Multiples of 20 = 20, 40, 60, 80 and so on.

LCM of 12 and 20 is 60.

HCF and LCM of two numbers are related to each other as well as with the given numbers. For any two numbers a and b, HCF (a, b) × LCM (a, b) = a × b.

HCF and LCM of Positve Integers

The product of HCF and LCM of the given positive integers suppose “m” and “n” is equal to the multiplication of the given numbers “m” and “n”. That is, HCF(m,n) × LCM (m,n) =m × n. Let us look at the example based on the above relation.

Example: Prove that the LCM (8, 12) × HCF (8, 12) = Product(8, 12)

Solution: LCM and HCF of 8 and 12: Multiples of 8 and 12 to find LCM is 8 = 8, 16, 24 , 32, 40 and so on, and 12 = 12, 24, 36, 48 and so on. LCM of 8 and 12 = 24. Now let us look at factors of 8 and 12. 8 = 2 × 2 × 2 12 = 2 × 2 × 3 HCF of 8 and 12 = 4. LCM (8, 12) × HCF (8, 12) = 24 × 4 = 96 Product of 8 and 12 = 8 × 12 = 96

Hence, LCM (8, 12) × HCF (8, 12) = Product(8, 12) = 96

HCF and LCM of Co-Prime numbers

LCM of Co-Prime numbers(m, n) = Product of two numbers (m, n). Since the HCF of co-prime numbers is equal to 1, the LCM of two co-prime numbers is the same as the product of the numbers. Look at the given example to verify the relation.

For example: 11 and 31 are two co-prime numbers. Let's verify LCM of given co-prime Numbers is equal to the product of the given numbers.
Solution: Factors of 11 and 31 are, 11 = 1 × 11 31 = 1 × 31 HCF of 11 and 31 = 1 LCM of 11 and 31 = 341 Product of 11 and 31 = 11× 31 = 341

We just verified that the LCM of co-prime numbers = Product of the numbers

HCF and LCM of Fractions

To find HCF and LCM of fractions like m/n, p/q, u/v, etc, we can use the below-mentioned formula:

LCM of fractions = LCM of Numerators ÷ HCF of Denominators
HCF of fractions = HCF of Numerators ÷ LCM of Denominators

Let's take two examples to understand it better.

Example 1: Find the LCM of the given fractions 1/4, 3/10, 2/5.

LCM of fractions = LCM of Numerators ÷ HCF of Denominators LCM of fractions = LCM (1,3,2) ÷ HCF(4,10,5) = 6 ÷ 1 = 6

Example 2: Find the HCF of the fractions 4/5, 5/2, 6/7.

HCF of fractions = HCF of Numerators ÷ LCM of Denominators

HCF of fractions = HCF (4, 5, 6) ÷ LCM (5, 2, 7) = 1 / 70

Given below is the image to summarize the relation between HCF and LCM.

Relation between HCF and LCM of 3 Numbers

In this section, we are going to learn the relation between HCF and LCM of three numbers. Suppose p,q,r are the three numbers, then to find LCM of these three numbers we will multiply the product of numbers (p×q×r) with HCF of numbers(p,q,r) and divide it by the product of HCF(p,q), HCF(q,r) and HCF(r,p). Similarly to find the HCF of p, q, r we will multiply the product of numbers (p×q×r) with LCM of numbers(p,q,r) and divide it by the product of LCM(p,q), LCM(q,r) and LCM(r,p). The below-mentioned formulae can be used to understand the relation and to calculate the HCF and LCM of 3 numbers.

\(LCM (p, q, r) = \dfrac{(p\times q\times r )\times HCF (p, q, r)}{HCF(p,q)\times HCF(q,r)\times HCF(r,p)}\)
\(HCF (p, q, r) = \dfrac{(p\times q\times r) \times LCM(p, q, r)}{LCM(p,q)\times LCM(q,r)\times LCM(r,p)}\)

Click here on the below links to learn more about the relation between HCF and LCM.

Example1: The HCF and LCM of two numbers are 8 and 336 respectively. If one of the numbers is 56, Find the other number.
Solution: We know HCF (of two numbers) × LCM (of two numbers) = product of two numbers Given, HCF of two numbers is 8, the LCM of two numbers is 336 and one of the numbers is 56. Applying the relation between HCF and LCM, we get, HCF (of two numbers) × LCM (of two numbers) = product of two numbers 8 × 336 = 56 × other number
Other number = 8 × 336 ÷ 56 = 48

Therefore, the other number is 48.

Example2: The LCM of two numbers 123 and 1681 is 5043. Find their HCF using the HCF-LCM relation.
Solution: HCF (123, 1681) × LCM (123, 1681) = Product of (123, 1681) Given, LCM of 123 and 1681 = 5043 HCF (123, 1681) = 123 ×1681 ÷ 5043

HCF (123, 1681) = 41

Therefore, the HCF is 41.

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FAQs on Relation Between HCF and LCM

The relationship between HCF and LCM of two given positive integers, let's say “m” and “n” is equal to the multiplication of the given numbers “m” and “n”, given as, HCF(m,n) × LCM (m,n) =m × n

What is LCM of Two Numbers?

The LCM or the least common multiple is the smallest natural number which is a multiple of two or more numbers. For two numbers, we can find the LCM by listing down all the multiples and then selecting the least common multiple of both. Another method is using the prime factorization method.

What is the Highest Common Factor?

The multiplication of common prime factors of given numbers with the least exponential powers is the highest common factor of two or more numbers.

What is the Relation Between HCF and LCM of co-prime numbers?

The Relation Between HCF and LCM of co-prime numbers is the product of the numbers = LCM of Co-Prime numbers, as the HCF of co-prime numbers is equal to 1.

What are H.C.F. and L.C.M. of Fractions?

The HCF and LCM of fractions is given as,

LCM of fractions = LCM of Numerators ÷ HCF of Denominators
HCF of fractions = HCF of Numerators ÷ LCM of Denominators

What is the Difference Between LCM and HCF?

The LCM of two or more numbers can be divided by the numbers and it is the smallest common multiple of those numbers. The greatest number that divdes the two or more numbers exactly is the highest common factor of those numbers. HCF of two numbers cannot be greater than the numbers, while LCM of two numbers is always greater than or equals to the larger number except 0 which is considered as the common multiple of every number.