Finding the least common multiple

  • Listing is very inefficient but shows the concept:
    • Two: 2, 4, 6, 8, 10, 12, ...
    • Three: 3, 6, 9, 12, ...
    • Written LCM(2,3) = 6

Quicker is similar to finding Finding the greatest common divisor:

  1. Find the prime factorization of each number
  2. Use a table or any organization method to list the prime factors of each number
  3. Generate a list that contains each prime factor.
  4. When a factor is repeated between two or more numbers, we only include the largest number of repeats from any of the prime factorizations
  5. The LCM is the product of the numbers in the list
  • 40 and 60
  • 40 = 2 x 2 x 2 x 5
  • 60 = 2 x 2 z 3 x 5
  • That's 5, 3 and the largest number of repeats of 2: 2 x 2 x 2 in 40
  • 5 x 3 x 2 x 2 x 2
  • LCM(40, 60) = 120
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Finding the least common multiple