Find HCF and LCM of 336 and 54 by prime factorization and verify that?

By Mandeep Kumar|Updated : May 16th, 2023

First we will find the HCF of 336 and 54 by prime factorization. For that it is important to determine the prime factors of 336 and 54.

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

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

Above, we can see that the common prime factors of 336 and 54 are 2 and 3.

Hence, the HCF of 336 and 54 by prime factorization is 2 × 3 = 6.

Now, let us look at the steps to find LCM of 336 and 54 by prime factorization. To find the LCM of 336 and 54 we have to multiply the prime factors of 336 and 54.

LCM of 336 and 54 = 2 × 2 × 2 × 2 × 3 × 7 × 2 × 3 × 3 × 3
Therefore, the LCM of 336 and 54 by prime factorization = 3024

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HCF and LCM of 336, 54 by Prime Factorization and Verification

As discussed above, the HCF of 336 and 54 by prime factorization is 2 × 3 = 6 and the LCM of 336 and 54 by prime factorization = 3024.

Now we have to verify the HCF and LCM. To do so, we will use the formula i.e.

HCF × LCM = Product of the two numbers

6 × 3024 = 336 × 54 (By putting the values in the formula)

18144 = 18144

Here, LHS = RHS. Hence verified.

Summary: