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# Least Common Multiples

## 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,.......

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

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

## Least common multiples(L.C.M):

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

## Methods of finding L.C.M:

• Prime factor method
• Steps:

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 therequired L.C.M.

• Common division method
• Steps:

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

2. Divide them by a suitable prime number, which exactly divides atleast 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.