What is the least common multiple of 10 16 and 24?

Answer 1

One way to solve this is to find the least common multiple of two of the numbers, and then find the least common multiple of that result with the third number. The least common multiple of two numbers is their product divided by their greatest common factor.
The greatest common factor of 10 and 16 is 2, so the least common multiple is 10 x 16 ÷ 2 = 80.
The greatest common factor of 80 and 24 is 8, so the least common multiple is 80 x 24 ÷ 8 = 240.
The least common multiple of 10, 16, and 24 is 240.

Another way to solve this is to find the prime factors of each number, then choose the highest power of each factor and multiply them together.
The prime factors of 10 are 2 and 5.
The prime factors of 16 are 2, 2, 2, and 2, which is 24.
The prime factors of 24 are 2, 2, 2, and 3, which is 23 and 3.
The highest power of 2 is 24, the highest power of 3 is 3, and the highest power of 5 is 5. So, the least common multiple is 24 x 3 x 5 = 16 x 3 x 5 = 240.