If LCM (72,126) $=$ 504, find HCF (72,126).

Given :

LCM of the two numbers 72 , 126 is 504.

To find :

We have to find the HCF of the two numbers 72 and 126.

Solution :

If x and y are two numbers, then,

$$LCM(x , y) \times HCF (x , y)  = Product of the two numbers (x \times y)$$

$LCM(72 , 126) \times HCF (72 , 126)  = 72 \times 126$

$504 \times HCF (72 , 126)  = 72 \times 126$

$HCF (72 , 126)  = \frac{72 \times 126}{504}$

$HCF (72 , 126)  = \frac{126}{7}$                             $[72 \times 7 = 504]$

$HCF (72 , 126)  = 18$                                                $[18 \times 7 = 126]$

Therefore,  HCF (72 , 126) is 18.

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Updated on: 10-Oct-2022

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