Daily Scribe
November 16, 2010
By Larisa Kreismanis
Today in class we learned about the differences between multiples and factors and how to find the least common multiple (LCM) of numeric expressions and variable expressions.
Multiples and Factors
Multiple- A multiple is a number(n) times another number continuing in a numeric pattern. For example,
The first five multiples of 8 are 8, 16, 24, 32, and 40.
Factor- A factor is a number that you can multiply by another number to get the number you need factors for. Factors can be whole numbers or fractions.
For example,
16 is a factor of 32 because 16*2=32
Least Common Multiple (LCM)
The least common multiple of a number is the smallest number that is a multiple of two or more numbers. You can find the least common multiple (LCM) by listing the multiples of the numbers and find which is the smallest multiple in common. For example,
The LCM of 12 and 20 is 60
Multiples of 12 – 12, 24, 36, 48, 60, 72
Multiples of 20 – 20, 40, 60, 80, 100
LCM= 60
Finding Least Common Multiple (LCM)
Using Prime Factorization
You can also find the LCM by using prime factorization. The least common multiple (LCM) is the smallest number that two numbers can be divided into. When finding the LCM by using prime factorization, you find the prime factorization for both numbers. Then you pick the set of prime factors that overlap each other and you multiply them by the numbers that do not overlap each other. The product of these numbers will then be the LCM. For example,
The LCM of 25 and 40 is 200.
Prime Factorization for 25= 5*5.
Prime Factorization for 40= 2*2*2*5.
5 is the only overlapping number, so to find the LCM you multiply 2*2*2*5*5=200.
Finding The Least Common
Multiple in Variable Expressions
When finding the LCM in variable expressions you find the prime factorization for both numbers. Then, including the variables, you pick the sets of numbers that overlap each other, then you multiply the sets of numbers and variables that overlap each other by numbers that do not overlap each other. For example,
The LCM of 15ab2 and 12abc is 60ab2c.
The prime factorization of 15ab2 = 3*5*a*b*b.
The prime factorization of 12abc = 2*2*3*a*b*c.
The overlapping numbers are 3,a,b so to find the LCM you multiply 2*2*3*5*a*b*b*c to get 60ab2c.
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