Least Common Multiples

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Least Common Multiples - PowerPoint PPT Presentation

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

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
• 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
• 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
• 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.