## 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.

- Rishi Jethwa
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