Question

The least common multiple of two integers is 240, and the greatest common divisor is 24. Given that one of the integers is 48, what is the other integer?

Answer 1

120

Explanation:

If you want the aops explanation:

The prime factorization of 48 is $2^4\cdot3$. Since the greatest common factor is 24, that means the other number also has the factors $2^3$ and 3 but not a fourth 2. When we divide 240 by 48, we get 5. The factors $2^3$ and 3 of the other number are covered by the factors of 48, but the factor 5 must come from the other number. So, the other number is $2^3\cdot3\cdot5=\boxed{120}$.

Answer 2

120

Explanation:

The computation of the other integer is shown below:

The Factor of 48 is 2^4 × 3

Also the greatest common divisor is 24,

This results that the second number also contains the factors 2^3 and 3 but not a fourth 2.

Now when there is a division of 240 by 48 so the number comes is 5

Now the second number factors are 2^3 and 3 that represents that it is under the factors of 48 but the factor 5 would arise from the second number

So, the other number is 120