Question

The product of two integers x and y is 2,17,728 and LCM(x,y)= 42 x HCF (x,y).
Find the HCF and LCM of x and y​

Answer 1

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Answer 2

Given info : The product of two integers x and y is 2,17,728 and LCM (x , y) = 42 × HCF (x, y)

To find : The HCF and LCM of x and y are ...

solution : a/c to question,

The product of two integers x and y is 2,17,728

i.e., x × y = 2,17,728 ....(1)

LCM (x, y) = 42 HCF(x , y) ....(2)

we know,

product of a and b = HCF (a , b) × LCM (a, b)

so, x × y = HCF (x ,y) × LCM (x , y)

from equations (1) and (2) we get,

⇒2,17,728 = HCF(x, y) × 42 × HCF(x, y)

⇒217728 = 42 × {HCF(x , y)}²

⇒{HCF(x , y)}² = 217728/42 = 5184 = (72)²

⇒HCF(x , y) = 72

and LCM = 42 × HCF(x, y) = 42 × 72 = 3024

Therefore LCM(x, y) and HCF(x , y) are 3024 and 72 respectively.