Bell Ringer 1. Find the LCM of 3 and 6 2. Find the GCF of 8 and 12

Last Night’s Homework Find the LCM & GCF 5 and 15 LCM- 15 GCF- 5

Homework Find the LCM & GCF 11 and 55 6 and 15 2 and 3

Becky Afghani, LBUSD Math Curriculum Office, 2003 Quick Check will be Wednesday!!! Over: LCM & GCF Becky Afghani, LBUSD Math Curriculum Office, 2003

Standard Number Sense (NS) 4 Find the common multiples of two whole numbers less than or equal to 12 and the common factors of two whole numbers less than or equal to 100.

One method to solve 3 things: LCM, GCF and Simplified Fractions The Ladder Method One method to solve 3 things: LCM, GCF and Simplified Fractions

The Ladder Method... is a method of factoring which allows you to factor two numbers at once in order to… find the LCM of the two numbers find the GCF of the two numbers simplify a fraction with these numbers as numerator and denominator

Use the ladder to factor 6 and 8 You will divide out any common factors of the two numbers 2 6 8 3 4 What number goes into both 6 and 8? Now divide both 6 and 8 by the 2 Does any # besides 1 go into both 3 and 4? No? Then you are done.

Let’s find the Least Common Multiple (LCM) of 6 and 8 The LCM is the product of all the numbers on the left and the bottom. x 2 6 8 The LCM of 6 and 8 is 24. 3 4 =24

Which numbers in the ladder give you the LCM? The “L” shape gives you the LCM: multiply the numbers on the left and bottom. # # # # # # # # # # #

What about the Greatest Common Factor (GCF) of 6 and 8? The GCF is the product of all the numbers on the left. 2 6 8 The GCF of 6 and 8 is 2. 3 4

Which numbers in the ladder give you the GCF? Multiply the numbers on the left only for the GCF. # # # # # # # # # # #

How can we use the Ladder Method to simplify ? The simplified numerator and denominator are on the bottom. simplifies to 2 6 8 3 4

Which numbers in the ladder give you the simplified fraction? The numbers on the bottom of the ladder are your simplified numerator and denominator. # # # # # # # # # # #

Let’s try some bigger numbers. Divide out all the common factors down the left side. 2 24 60 What number goes into both 24 and 60? Does any # besides 1 go into both 12 and 30? 2 12 30 How about 6 and 15? Anything else? 3 6 15 No? You’re done. 2 5

= 120 24 60 2 12 30 6 15 3 5 Find the LCM. The LCM of 24 and 60 x The LCM of 24 and 60 is 120. 24 60 2 12 30 6 15 3 5 = 120

= 12 24 60 2 12 30 6 15 3 5 Find the GCF. The GCF of 24 and 60 is 12. x The GCF of 24 and 60 is 12. 24 60 2 12 30 6 15 3 5 = 12

Simplify . simplifies to . 24 60 2 12 30 6 15 3 5

You Try Find the LCM, GCF, and Simplify. 5 and 30 18 and 24 7 and 49 1. 5 & 30 2. 18 & 24 3. 7 & 8 4. 1 &3

Find the LCM, GCF, and Simplify. T.O.T.D Find the LCM, GCF, and Simplify. 18 and 30 5 and 100