Multiples of a given number are numbers that are obtained when we multiply the given number with an integer. A number can have infinite multiples.

**For example:**

The multiples of 2 are 2, 4, 6, 8, 10, 12 and so on. That is all the numbers that appear in the table of 2.

The multiples of 5 are 5, 10, 15, 20, 25 and so on.

Multiples of 10 are 10, 20, 30, 40, 50 and so on.

**More about multiples**

Every number is a multiple of 1.

Every number is a multiple of itself. In fact, the first multiple of any number is the number itself.

0 is a multiple of every number.

**Practice questions**

Question: Find the first 5 multiples of the number 12.

( Answer: First 5 multiples of 12 are 12, 24, 36, 48, 60 )

Question: Find the first 5 multiples of the number 4.

( Answer: First 5 multiples of 4 are 4, 8, 12, 16, 20 )

Question: Find the first 3 multiples of the number 16.

( Answer: First 3 multiples of 16 are 16, 32, 48 )

Question: Find the factors and first 5 multiples of the number 10.

( Answer: Factors of 10 are 1, 2, 5, 10

First 5 multiples of 10 are 10, 20, 30, 40, 50

)

**Common multiples**

If we multiply two numbers, then the obtained product is a common multiple of the two numbers.

For example: If two numbers 3 and 8 are multiplied then the result 24 is a common multiple of 3 and 8.

The Least common multiple or LCM of two or more numbers is the smallest number that is a multiple of all the numbers.

The LCM is useful in solving many maths problems.

**Practice questions**

Question: Find the least common multiple of 3 and 4.

( Answer: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27...

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

Common multiples of 3 and 4 are : 12, 24..

Least common multiple of 3 and 4 is 12

)

Question: Find the least common multiple of 3 and 5 and 6 .

( Answer: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33...

Multiples of 5 = 5, 10, 15, 20, 25, 30, 35…

Multiples of 6 = 6, 12, 18, 24, 30, 36...

Least common multiple of 3, 5 and 6 is 30

)

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