# Grade 5, Maths Olympiad (CBSE) - Multiples

## Multiples

The numbers we get by multiplying a given number are called multiples of the given number. These are essentially the numbers found in multiplication table of the number.

The smallest multiple of a number is the number itself. Biggest multiple of a number is very big and can't be determined. Multiples of a number are unlimited.

*Factors of a number are limited and biggest factor of a number is the number itself.

E.g.

Multiples of 6 are 6 X 1, 6 X 2, 6 X 3, 6 X 4 , 6 X 5, 6 X 6 etc.

or we can say 6, 12, 18, 24, 30, 36 etc. are multiples of six.

Common multiples: The multiples which are common between 2 numbers are called multiples. Common multiples of two numbers are infinite.

L.C.M. or lowest common multiple: The lowest number between the common multiples of two numbers is called the L.C.M. of two numbers.

E.g.

Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72 etc

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 etc

24, 48 and 72 and so on are common multiples of 6 and 8. 24 is the lowest common multiple so it is the L.C.M. of 6 and 8.

Imp Concept:

Rules of divisibility

1. If a number is even it is divisible by 2.
2. A number is divisible by 3 if the sum of the digits of the number is divisible 3. E.g. Is 4635 divisible by 3? 4 + 6 + 3 + 5=18. 18 is divisible by 3 so the number 4635 is divisible by 3.
3. A number is divisible by 4 if the number formed by its last two digits is divisible by 4. E.g. to check if 47932 is divisible by 4, check if last 2 digits 32 is divisible by 4. Yes, 32 is divisible by 4 so the number 47932 is divisible by 4.
4. If a number has 0 or 5 as the last digit then the number is divisible by 5.
5. A number is divisible by 9 if the sum of the digits of the number is divisible by 9. E.g. Is 4635 divisible by 9? 4 + 6 + 3 + 5=18. 18 is divisible by 9 so the number 4635 is divisible by 9.
6. A number is divisible by 10 if the last digit is 0. 