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# 6th Grade - GCF and LCM

## Introduction

• GCF stands for "Greatest Common Factor". To find the GCF of the given numbers, list all the factors of the given numbers and then find the largest common factor.
• LCM stands for "Least Common Multiple". To find the LCM of the given numbers, list the multiples of the given numbers until you find the smallest common multiple.

## Examples of GCF and LCM

Example 1: Find the GCF of 36 and 54.

Factors of 36 :

Factors of 54:

The greatest common factor is 18.

Example 2: Find the GCF  of 49 and 63.

Factors of 49:

Factors of 63:

The greatest common factor is 7.

Example 3: Find the LCM of 12 and 9.

Multiples of 12: 12, 24, 36, 48, 60

Multiples of 9: 9, 18, 27, 36, 45

The least common multiple is 36.

Example 4: Find the LCM of 24 and 36.

Multiples of 24: 24, 48, 72, 96

Multiples of 36: 36, 72, 108

The least common multiple is 72.

## Cheat Sheet

• GCF is the largest common factor of all the possible factors of the given numbers.
• LCM is the smallest common multiple of the given numbers.
• Being able to recognize the GCF and LCM of given numbers comes in handy when performing operations with fractions.
• LCD stands for the least common denominator.
• LCD of the given fractions is the LCM of the denominators of the given fractions.
• Example of the use of GCF in daily life: distributing items equally into groups without any leftovers
• Examples of the use of LCM in daily life: to find out when the bikers riding a bike in a loop at different speeds will meet, or a train running at different speeds will cross.

## Blunder Area

• LCM should not be confused with GCF.