Verify the relationship between HCF and LCM of: 64, 84.

Given: 64 and 84.

To verify: Here we have to verify the relationship between HCF and LCM of: 64, 84.

Solution:

Relationship between HCF and LCM is as follows;

HCF $\times$ LCM = Product of those two numbers

So, calculating LCM and HCF of 64 and 84.

Prime factorization of 64 and 84;

64 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 = 2⁶

84  = 2 $\times$ 2 $\times$ 3 $\times$ 7 = 2² $\times$ 3 $\times$ 7

Therefore,

LCM (64,84) = 2⁶ $\times$ 3 $\times$ 7 = 1344

HCF (64,84) = 2² = 4

Now,

HCF $\times$ LCM = Product of those two numbers

4 $\times$ 1344 = 64 $\times$ 84

5376 = 5376

So, relationship between HCF and LCM of 64, 84 is verified.

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Updated on: 10-Oct-2022

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