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 nu

Question

3 years ago

5

mber if one of its factors is 9.

1 answer:

12345 [234] · Answer 1 · 2022-05-20T00:05:24+03:00

Answer:

The third number is 180.

Step-by-step 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.