Question

What is the smallest positive integer that is a multiple of both 24 and 45?

Answer 1

You can find that by finding the lcm, or using the lcm function included with many graphing calculators if you have.

LCM is 360

Answer 2

To find the smallest positive integer that is a multiple of both 24 and 45, we can find the least common multiple (LCM) of the two numbers.

Prime factorizing 24, we get: 2^3 x 3^1
Prime factorizing 45, we get: 3^2 x 5^1

To find the LCM, we take the highest power of each prime factor that appears in either factorization:

2^3 x 3^2 x 5^1 = 360

Therefore, the smallest positive integer that is a multiple of both 24 and 45 is 360.