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The Least Common Multiple and Highest Common Factor of two numbers are 60 and 4 respectively. If their sum is 32, then what will be the difference of these two numbers?

The Least Common Multiple and Highest Common Factor of two numbers are 60 and 4 respectively. If their sum is 32, then what will be the difference of these two numbers? Correct Answer 8

Given:

LCM = 60

HCF = 4

Sum of numbers = 32

Formula used:

Product of two numbers = LCM × HCF

Calculation:

Let the two number be x and y

So x × y = 60 × 4 = 240      ---- (i)

We know that,

(x – y)2 = (x + y)2 – 4xy

⇒ (x – y)2 = 322 – 4 × 240

⇒ (x – y)2 = 1024 – 960

⇒ (x – y)2 = 64

⇒ x – y = 8

∴ Difference of these two numbers = 8

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