Download Least Common Multiples

Least Common
Multiples
S
Multiples
S Multiples are the product of a number and any whole number.
S LCM- least common multiple- the least multiple common to all
numbers.
S Find by:
S List the multiples
S Ex 1: 6 and 9:
S
S
S
6: 6,12,18,24,30, 36,42,48
9: 9,18,27,36, 45,54,63,72,81
LCM: 18
S Ex. 2: Find by method 2:
S Find the prime factorization of two numbers.
Write each prime factor the greatest number of
times it occurs for any of the digits.
S 4,14: 4= 2x2; 14= 2x7: So 2 occurs twice, 7
occurs once:
S So 2x2x7=28, 28 is the least common
multiple.
Uses of LCM
S Finding LCM of algebraic terms:
S Ex:3
S 35x^2 and 175xy
S 35x^2= 5*7*x*x
S LCM=5*5*7*x*x*y
175 = 7*5*5*x*y
LCD: Least Common
Denominator
S The LCD will be the LCM of the Denominator:
S Ex. 4:
S 1/12, -3/16, 5/18
S Find LCM of 12, 16,18:
12=2*3*2
S 16=2*2*2*2
S 18=2*3*3
S Multiply 2*2*2*2*3*3=144
S
You can also used the LCD for
ALGEBRAIC fractions
S Ex. 5: Find LCD for the following
S 6c/5b; 2c/15b, 7c/25b
S 5b=5*b
S 15b=3*5*b
S 25b=5*5*b
S 3*5*5*b=75b
S LCD is 75b
S DO 1-10 in notebook now.