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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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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
slide3

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.
uses of lcm
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
lcd least common denominator
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
you can also used the lcd for algebraic fractions
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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