lcm /common factor

[mariah]

Least multiple of A and B is 120, and A/B= 3:4. What is the greatest comon factor?

oa 10

it took me around 5 minutes, any shortcusts?

[DeepakR]

The product of two numbers is equal to the product of LCM and GCD of the two numbers. Let the numbers be 3x and 4x. Hence LCM = 12x = 120. Therefore x=10 and the numbers are 30 and 40.

Now 30 * 40 = 120 * GCD so GCD = 10.

- Deepak

[sureshbala]

In order to answer this there is no need to calculate the numbers.

Let the numbers be 3p and 4p.

It is clear that GCD of these numbers is p.

We have LCM x GCD = Product of the numbers.

So 120 x p = 12p^2

So p = 10 which is the GCD