In order to learn about HCF (highest common factor) and LCM (least common multiple), one should know about two important concepts: factors and multiples. Without the prior knowledge of factors and multiples, one cannot understand LCM and HCF questions (by HCF division method).

## What are factors and why they are important for LCM and HCF questions?

Factor is such a number which when comes in the table of a specific number, then all those numbers will be called as that numberâ€™s factor.

For instance, if we have a number 15, so 15 comes in the tables of which numbers? Clearly, 15 comes in the table of **1 **(1 x 15=15), **3** (3 x 5=15), **5** (5x 3=15), and** 15** itself (15×1=15). Thus, the factors of 15 are 1, 3, and 5. *(We will not write 15 because it has already been represented by 1). *

**Always remember that 1 is the factor of all numbers.**

### How to find factors of a number through HCF division method?

### How to find factors of a number?

The easiest way to find the factors of a number is by the divisional method. This method can be understand with help of an example.

Example: Find factors of 15. 5 15 3 3 1 Factors of 15 = 1 x 3 x 5

## What are multiples and why they are important for LCM and HCF questions?

All numbers that comes in the table of a number are its multiples. For example, multiple of 15 are 15, 30, 45…, and so on.

### How to find multiples of a number?

In order to find multiples of a number, just use the multiplication tables.

## What is HCF and how to calculate HCF of a number (HCF division method)?

## What is HCF and how to calculate HCF of a number?

HCF is the largest of all the common factors. It is also called GCD (Greatest Common Divisor or Greatest Common Denominator). HCF can be calculated with help of a formula which is:

**HCF = product of common factors**

The best way to understand HCF calculation is by example.

Find the HCF of 24 and 36. Solution: 2 24 2 36 2 12 2 18 2 6 3 9 3 3 3 3 1 1 Factors of 24 = 1 2 2 2 3 Factors of 36 = 1 2 2 3 3 Common Factors = 1 x 2 x 2 x 3 = 12 HCF = Product of common factors = 12

**What is LCM and how to calculate LCM of a number through HCF division method?**

## What is LCM and how to calculate LCM of a number?

LCM is the smallest number that is a multiple of two or more numbers. It is the abbreviation of least common multiple. LCM can be calculated with the help of a formula which is:

**LCM = common factors x uncommon factors**

or

**LCM = HCF x All other factors** *(in special cases)*

The best way to understand LCM calculation is with the help of an example.

Find the LCM of 144 and 232. Solution: 2 144 2 232 2 72 2 116 2 36 2 58 2 18 29 29 3 9 1 3 3 1 Factors of 144 = 1 2 2 2 2 3 3 Factors of 232 = 1 2 2 2 29 Common Factors = 1x2x2x2 = 8 Uncommon Factors= 2x3x3x29 = 522 LCM = Product of common x uncommon factors = 8 x 522 = 4176

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