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How to Find the Least Common Multiple Using a Factor Tree

Prime numbers are numbers that can only be divided by 1 and themselves. The lowest prime numbers are 2, 3, 5, 7, 11, 13 and 17. Prime factorization is a process where a larger number is broken down into its prime number multiples. This is done when trying to find the least common multiple, or factor, between two large numbers. When first learning to work with prime factorization, a factor tree serves as a handy visual aid to make sure the math is accurate.

Instructions

- 1
  Find the least common multiple of two numbers by first breaking down each number into its prime factors, listing them in a tree format. Use the numbers 72 and 66 as an example problem.
- 2
  Write 66 on the top left side of a piece of paper. Draw two diagonal lines down to the next line where you'll write the first factors, 11 and 6 since 11 multiplied by 6 equals 66 and 11 is already a prime numbers. Draw two diagonal lines down from the 6 to divide it into prime numbers, 3 and 2 since 3 multiplied by 2 equals 6.
- 3
  Write 72 on the top right side of the paper with two diagonal lines extending down. Write 9 and 8 since they are easy factors, though not prime, to find for this number. Draw two lines extending below the 9 and break it down to 3 and 3 since 3 multiplied by 3 equals 9. Draw two lines below the 8 and break it into 2 and 4, since 2 multiplied by 4 equals 8. Draw two lines below the 4 to finish the factorization with 2 and 2.
- 4
  The factors of 66 are 11, 3 and 2 while the factors of 72 are 3, 3, 2, 2 and 2. Create an expression that multiplies each factor by the maximum number of times it appears in either factorization: 11 * (3 * 3) * (2 * 2 * 2) because 11 appears once in 66, 3 appears twice in 72 and 2 appears three times in 72.
- 5
  Solve the expression: 11 * (3 * 3) * (2 * 2 * 2) = 11 * 9 * 8 = 792. Write that the least common multiple of 72 and 66 is 792.

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