Least Common Multiple.

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Presentation transcript:

Least Common Multiple

(1) MANUAL METHOD Example: find the least common multiple of 10 and 15 To find the Least Common Multiple of two numbers: Write the multiples of each number Select the common ones Choose the least Example: find the least common multiple of 10 and 15 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ….. Multiples of 15: 15, 30, 45, 60, 75, 90….. We take the least one, so LCM(10,15) = 30

LCM(4, 12) = 12 LCM(4, 12,8) = 24 Exercise 1: find the LCM (4, 12) Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…. Multiples of 12: 12, 24, 36, 48, 60, 72,…… LCM(4, 12) = 12 Exercise 2: find the LCM (4, 12, 8) Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…. Multiples of 12: 12, 24, 36, 48, 60, 72,…… Multiples of 8: 8, 16, 24, 32, 40,48, 56 …. LCM(4, 12,8) = 24

= 24 (2) PRIME FACTORIZATION METHOD LCM(4, 24) = To find the Least Common Multiple of two numbers: Write the PRIME FACTORIZATION of each number Select all the factors with the BIGGEST exponent Multiply them Example: find the least common multiple of 4 and 24 Write the prime factorization of 4 and 12: LCM(4, 24) = = 24

Exercise 3: find the LCM (20, 30)

Exercise 4: find the LCM (20, 30, 45) = 180

Exercise 5