Intro to Algebra/Geometry

Least Common Multiple

Multiple

The product of any number and an integer

The Multiples of 2:2x1=2, 2x2=4, 2x3=6, 2x4=8, 2x5=10, …

Common

To say that things have something in common we mean that they share the same thing. When we say multiples are common then they have the same multiples.

Multiples of 2:2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, . . .

Multiples of 3:3, 6, 9, 12, 15, 18, 21, 24, . . .

Least Common Multiple

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

Multiples of 3:3, 6, 9, 12, 15, 18, 21, 24, 27, . . .

Multiples of 4:4, 8, 12, 16, 20, 24, 28, . . .

The LCM of 3 and 4 is 12

Find the LCM

1. 4 and 5

2. 4 and 8

3. 3 and 8

Make a Factor Tree

You can rewrite Numbers as a Product of Prime Numbers by using a Factor Tree.

Finding the LCM using the Factor Tree

1. Write out the Numbers as a product of Prime Factors (ex. 18 = 2 x 3 x 3)

2. Use every factor that is available and use the most possible

3. Multiply the factors together

Use the Product of Primes to Find LCM

35: 7 x 545: 3 x 3 x 5

LCM: 3 x 3 x 5 x 7 = 315

Find LCM using the Product of Primes

1. 6 and 8

2. 7 and 24

3. 33 and 4