If HCF (336, 54) = 6, find LCM (336, 54)

By Mandeep Kumar|Updated : May 22nd, 2023

Given: HCF (336, 54) = 6

To find: LCM of 336 and 54

The LCM of 336 and 54 can be determined by using the relation LCM × HCF = Product of two numbers. We have to put the given values in this formula to find the answer.

We have the two numbers that are 336 and 54.

The value of HCF = 6.

LCM × HCF = Product of two numbers

LCM × 6 = 336 × 54

LCM × 6 = 18144

LCM = 18144 ÷ 6

LCM = 3024

So, the LCM of 336 and 54, for which the HCF is 6, is 3024.

LCM of 336 & 54 whose HCF is 6

The answer can be determined by the prime factorization method also. The prime factoriszation of 336 and 54 can be done in the following way to get the LCM of 336 and 54.

Prime Factorization of 54 = 2 × 3 × 3 × 3 and

Prime Factorization of 336 = 2 × 2 × 2 × 2 × 3 × 7

Here the prime factors of 54 are 2 × 3 × 3 × 3 or (2 × 33) and the prime factors of 336 are 2 × 2 × 2 × 2 × 3 × 7 or (24 × 3 × 7). Now to get the LCM of these two numbers, we have to multiply the prime factors of 336 and 54.

So, the LCM of 336 and 54 = 2 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 3 × 7 = 3024.

Summary:

If HCF (336, 54) = 6, find LCM (336, 54)

If HCF (336, 54) = 6, then the LCM of 336 and 54 is 3024. By using the relation of Product of two numbers = LCM × HCF, LCM of the given numbers can be found easily. LCM is the least common multiple of the two or more numbers.

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