YOU TRY 1 Find the least common multiple of: a) 6 and 9. b) 3, 9, and 12. Note The least common multiple of a group of different prime numbers is always the product of the primes. Example: The numbers 5 and 7 are prime. Their LCM is 5 7 35. If the numbers are easy to work with, we should be able to fi nd the LCM without making a list or writing anything on paper. Find the least common multiple of 4 and 10 by inspection. Solution Ask yourself, “What is the smallest number that is divisible by both 4 and 10?” That number is 20. Therefore, the LCM of 4 and 10 is 20. Find the least common multiple of 4 and 8 by inspection. We can also fi nd the LCM by fi rst fi nding multiples of the larger number and then fi nding the smallest of those that is divisible by the other numbers in the group. Find the least common multiple of 12 and 16 by fi rst making a list of multiples of the larger number. Solution The larger of the two numbers is 16, so make a list of some multiples of 16. Multiples of 16: 16, 32, 48, 64, 80, … Are any of the numbers on the list divisible by 12? Yes! 48 is divisible by 12. The LCM of 12 and 16 is 48. EXAMPLE 2 YOU TRY 2 EXAMPLE 3 Which process do you find easiest to use? YOU TRY 3 Find the least common multiple of 15 and 20 by fi rst making a list of multiples of the larger number. www.mhhe.com/messersmith SECTION 4.2 Least Common Multiples 231
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