To find the least common multiple of two numbers, factor the two numbers, noting the frequency of the prime factors, and then multiply the most repeated factors together. Perform division to check your answer when complete.
- Determine the prime factors of the two numbers
Factor the two numbers in the equation until the factors are only prime numbers. For example, to find the least common multiple of 18 and 24, first determine the prime factors of 18 (3 x 3 x 2), and then find the prime factors of 24 (3 x 2 x 2 x 2).
- Note the most common prime numbers
Underline the factors that appear most frequently in each prime factorization.
- Multiply all of the prime factors you underlined together and solve
Write an equation that finds the product of the frequent prime factors, and multiply these numbers together. Using the example from Step 2, the equation would be 3 x 3 x 2 x 2 x 2. Therefore, the product and the least common multiple of 18 and 24 is 74.
- Check your work
Check the work by dividing the least common multiple by both of the factors. The answer should be a positive and whole number.