# LCM & HCF YouTube Lecture Handouts

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## LCM & HCF Story with Tree & Circles

Mayank explains the following two key concepts to quickly and easily identify and solve all HCF and LCM problems - 1. Quickly find HCF and LCM using 3 simple tricks in this video. 2. To detect HCF and LCM word problems, use the following keywords: **LCM** 1. Minimum number of days, rounds etc. 2. Least amount of time, things etc. 3. Smallest number, length, amount of time etc. **HCF** 1. Maximum (possible) number of days, things etc. 2. Longest (possible) size, length, amount of time etc.

## Our Journey

- Factors
- Prime Factors

- Multiples
- Factors and Multiples
- Highest Common Factor
- Common Factors

- Least Common Multiple
- Common Multiples

**Understanding Factors**

## Prime Factors

- Factors which are prime (numbers) are called prime factors

## Understanding Multiples

## Factors and Multiples

*Factors*can (completely)*divide*the number

< Number

*Multiples*are (completely)*divisible*by the number.

> Number

## Factorization Using Tree of Factors

## Tree of Factors- 24

## Common Factors of 32 and 24

## Finding Common Factors (HCF) Using Grouping

Common Multiples of 32 and 24

32 … 32, 64, 96, 128, 160,192, 224, …

24 … 24, 48, 72, 96, 120, 144,168, 192, …

Least Common Multiple - LCM

Lowest common Factor – LCM

Highest Common Multiple - HCH

## HCF and LCM Combining the Two Steps

## Other Names of HCF

- Greatest Common Factor - GCF
- Greatest Common Divisor - GCD

Why Prime Factors?

✍ Mayank