Question

The product of two numbers is 7168
and their HCF is 16, find their LCM​

Answer 1

$\huge{\bold{\pink{\underline{\underline{\red{Solution:-}}}}}}$

Let us say that the numbers are x and y.

Both of them are multiples of 16 as their HCF is 16

So, we can say that they are 16a and 16b.

Also, HCF (a,b) = 1. They have no factor in common otherwise the HCF of 16a and 16b won't be 16. In other words, a and b are coprime to each other.

x * y = 7168

=> 16a * 16b = 7168

=> a * b = 28

Now, we need to split 28 into coprime factors

28 = 1*28 or 4*7

=> (x, y) = (16, 448) or (64, 112)

So, there are two pairs that satisfy the given conditions.