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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


  • 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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