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Least Common Multiples

Least Common Multiples. Multiples. Multiples are the product of a number and any whole number. LCM- least common multiple- the least multiple common to all numbers. Find by: List the multiples Ex 1: 6 and 9: 6: 6,12,18,24,30, 36,42,48 9: 9,18,27,36, 45,54,63,72,81 LCM: 18.

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Least Common Multiples

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  1. Least Common Multiples

  2. Multiples • Multiples are the product of a number and any whole number. • LCM- least common multiple- the least multiple common to all numbers. • Find by: • List the multiples • Ex 1: 6 and 9: • 6: 6,12,18,24,30, 36,42,48 • 9: 9,18,27,36, 45,54,63,72,81 • LCM: 18

  3. Ex. 2: Find by method 2: • Find the prime factorization of two numbers. Write each prime factor the greatest number of times it occurs for any of the digits. • 4,14: 4= 2x2; 14= 2x7: So 2 occurs twice, 7 occurs once: • So 2x2x7=28, 28 is the least common multiple.

  4. Uses of LCM • Finding LCM of algebraic terms: • Ex:3 • 35x^2 and 175xy • 35x^2= 5*7*x*x 175 = 7*5*5*x*y • LCM=5*5*7*x*x*y

  5. LCD: Least Common Denominator • The LCD will be the LCM of the Denominator: • Ex. 4: • 1/12, -3/16, 5/18 • Find LCM of 12, 16,18: • 12=2*3*2 • 16=2*2*2*2 • 18=2*3*3 • Multiply 2*2*2*2*3*3=144

  6. You can also used the LCD for ALGEBRAIC fractions • Ex. 5: Find LCD for the following • 6c/5b; 2c/15b, 7c/25b • 5b=5*b • 15b=3*5*b • 25b=5*5*b • 3*5*5*b=75b • LCD is 75b • DO 1-10 in notebook now.

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