Least Common Multiples Number Theory Number Theory number theory is the study of a set of positive numbers. Also known as natural numbers

example:

1, 2, 3, 4, 5, 6, 7, 8, 9 ect... Least Common Multiples Examples

of methods

on how to find LCM There are several methods you can use to

find the Least Common Multiple

find the multiples of two given numbers by:

1. use the method of listing each number

multiples

2. use the method of a prime factorization tree

3. use a number line You can make a list of (35 and 70) multiples to find the LCM

Set of multiples of 70 is (1x70, 2x70, 3x70, 4x70, 5x70, 6x70, 7x70, 8x70 9x70, 10x70 ...)

Set of multiples of 35 is (1x35, 2x35, 3x35, 4x35, 5x35, 6x35, 7x35, 8x35, 9x35 10x35 ...)

Answer: A={70, 140, 210, 280, 350, 420, 490, 560, 630, 700}

Answer: B={35, 70, 105, 140, 175, 210, 245, 280, 315, 350}

A∩ n B ={70, 140, 210, 280, 350...}

LCM (35, 70) =70 Factor tree http://www.fun4thebrain.com/beyondfacts/lcmsnowball.html Video math is

fun number line Sources:

YouTube.com www.wpclipart.com/education

www.fun4thebrain.com www.illustrationsof.com

www.shutterstock.com www.graphicfactory.com

www.clipart.com two natural numbers (n and m) is the smallest value of a number (h), so that h is a multiple of both m and n. http://www.factmonster.com/ipka/A0933352.html hyperlinks http://www.mathsisfun.com/least-common-multiple.html multiplication What do you know: 35 70 LCM=70 70 140 210 280 350 420 490 560 630 700 70 35 70 105 140 175 210 245 280 315 350 140 210 350 Helpful

websites What do we want to know about multiples Multiples grow You start with a number like 4

the multiples form by multiplying it with other numbers like 1, 2, 3, ect..

Or

you can think of it like adding groups of 4. The multiple will grow if you continue to add groups of 4

example: 4 items in one group equal 4 Prime Factorization two groups with 4

items in each group

equals 8 So,

4 and 8

are multiples of

4 Citation Is the breaking down of a given composite number

into the product of its prime factors.

Look at the two factors, check to see if one or both are prime numbers.

If it is not a prime number repeat the process This method can be used to find the LCM of a set of two or more numbers.

The intersection of two sets like A and B is the set that contains all elements of A that also belong to B. What do we know Build-up Method

This is another process of finding LCM This method express numbers like 24 and 36 in

their prime factor exponential form Example: 24=2x2x2x3 exponential form is 24=2ˆ3 x 3

36=2x2x3x3 exponential form is 36=2ˆ2 x 3ˆ2

Next step: Using the build-up method, compare 24 and36

24=2ˆ3 x 3

36=2ˆ2 x 3ˆ2

this has more threes than 2ˆ3 x 3

So, build up the 2ˆ3 x 3 to have the same number of threes

as 2ˆ2 x 3ˆ2. So, this makes the LCM 2ˆ3 x 3ˆ2 The process of set intersection Bennett, A, Burton, L, & Nelson, T (2012). Mathematic

for Elementary Teachers

(9ed.,). McGraw-Hill.

New York:

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