Question

The LCM of three numbers is 7920 and their GCD is 12. Two of the numbers are 48 and 264. Using factor notation find the third number if one of its factors is 9.

Answer 1

The third number is 180.

Explanation:

Let the third number be 9x where x is an integer.

48 = 2*2*2*2*3

264 = 2*2*2*3*11

9x = 3*3*x

2*2*2*2*3*3*11*x = 7920y where y is an integer

1584x = 7920y

so x = 7920y / 1584= 5y.

Now the GCD is 12 so x must have 4 as one of its factors.

Also x is a multiple of 5 so it could be 20 then y would be 4.

If x = 20 then the third number is 9*20 = 180.

This checks out OK.