What is the least common multiple of 10 14 and 55?

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 14 is 2, so the least common multiple is 10 x 14 ÷ 2 = 70.
The greatest common factor of 70 and 55 is 5, so the least common multiple is 70 x 55 ÷ 5 = 770.
The least common multiple of 10, 14, and 55 is 770.

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 14 are 2 and 7.
The prime factors of 55 are 5 and 11.
Among the prime factors of the three numbers, the highest power of 2 is 2, the highest power of 5 is 5, the highest power of 7 is 7, and the highest power of 11 is 11. So, the least common multiple of 10, 14, and 55 is 2 x 5 x 7 x 11 = 770.