Question

Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?

Answer 1

Let the first number be 2x and the second be 3x

∴ Their LCM = 2 × 3 × x

But given LCM = 180

∴ 2 × 3 × x = 180

`\implies` x = 30

First number = 2x = 2 × 30 = 60 = 2 × 2 × 3 × 5

Second number = 3x = 3 × 30 = 90 = 3 × 3 × 2 × 5

Now, HCF of 60 and 90 = 2 × 3 × 5 = 30