# Least Common Multiples - LCM

Before knowing Least Common Multiples (LCM) you must know what multiples are.

## Multiples

Multiples of a given numbers are all those numbers which can be divided completely by the given number.

### Example

Multiples of 4 are 4, 8, 12, 16....etc.

## Common Multiples

Common multiples of two or more numbers are the numbers which can exactly be divided each of the given numbers.

## Example:

Multiples of 3 are 3, 6, 9, 12, 15, 18, 2, 24 and so on.

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28 and so on.

.'. Common multiples of 3 and 4 = 12, 24 and so on.

## Least common multiples (LCM)

The least common multiples of two or more given numbers are the least number which is exactly divisible by each of the given numbers.

## Methods of finding LCM

## Prime factor method

1. Resolve each given number into its prime factors and express the factor obtained in exponent form.

2. Find the product of the highest powers of all the factors that occur in any of the given numbers.

3. The product obtained in step2 in the required L.C.M.

## Common division method

1. Write the given numbers in a horizontal line, separating them by commas.

2. Divide them by a suitable prime number, which exactly divides at least two of the given numbers.

3. Write down the quotients and the undivided numbers (if any) in step 2 in a line below the first.

4. Repeat the process until we get a line of numbers which are prime to one another.

5. The product of all the divisors and the numbers in the last line will be required L.C.M.

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