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 : $1, 2, 3, 4, 6, 9, 12, \mathbf{18}\mathbf{,} \mathrm{and} 36$

Factors of 54: $1, 2, 3, 6, 9, \mathbf{18}, 27, \mathrm{and} 54$

The greatest common factor is 18.

 

Example 2: Find the GCF  of 49 and 63.

Factors of 49: $1 \mathrm{and}\mathbf{ }\mathbf{7}$

Factors of 63:$1, \mathbf{7}, 9, \mathrm{and} 63$

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.