Find the LCM of Denominators: Calculating Least Common Multiple of 8, 10, and 12

Question

Given several denominators, what is their least common multiple?

81012 \boxed{8} \boxed{10} \boxed{12}

Step-by-Step Solution

The least common multiple (LCM) of 8,10, and 128, 10, \text{ and } 12 is the smallest positive integer that is divisible by each of these numbers.

List the multiples for reference:

  • Multiples of 88: 8, 16, 24, 32, 40, 48, 56, 64, ...
  • Multiples of 1010: 10, 20, 30, 40, 50, 60, ...
  • Multiples of 1212: 12, 24, 36, 48, 60, ...

The common multiples of 8,10, and 128, 10, \text{ and } 12 are 60, 120, ...

The smallest common multiple is 6060.

Answer

60