Question

Three numbers are in the ratio of 3:5:10, if LCM is 630 find hcf​

Answer 1

SOLUTION

Given:

Ratio of three numbers = 3 : 5 : 10

LCM of three number = 630

Formula:

If N is divided into a : b, then

First part = N × [a/(a + b)]

Second part = N × [b/(a + b)]

Calculation:

Ratio of three number = 3x : 5x : 10x

First number = 3x

Second number = 5x

Third number = 10x

3x = 3 × x

5x = 5 × x

10x = 10 × x

⇒ LCM of 3x, 5x and 10x = 2 × 3 × 5 × x = 30x

⇒ HCF of 3x, 5x and 10x = x

According to the question

30x = 630

⇒ x = 630/30

⇒ x = 21

∴ HCF of three numbers is 21

I hope it will be helpful for you.