Least Common Multiple (L.C.M )

Least Common Multiple (L.C.M )

L.C.M of two or more given numbers is the smallest number which is divisible by all the given numbers.

Multiples

How many steps can a rabbit jump if it is jumping 4 steps for 10 times?

4, 8, 12, 16, 20, 24, 28, 32, 36, 40

If we add 4 to each number we will get 40.

Try this

5, 10, 15, 20, 25, 30,35, 40,

Do you know?

Each number is the first multiple of that number.

There is a relation between the multiples and multiplication table of a number.

Common Multiples:-

The Multiples that are common to two numbers are their common multiples.

Example

Find the common multiples of 9, 12

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90,...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120,...

The common multiples of 9, 12 are 36, 72,….

Example

Find L.C.M of 4 and 6

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36,...

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54,...

Common multiples of 4, 6 are 12, 24, 36,.....

L.C.M of 4, 6 is 12.

Try this

Find L.C.M

1. 10 and 15

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90…

Multiples of 15: 15, 30, 45, 60, 75, 90…

Common multiples of 10 and 15 are 30, 60, 90…..

LCM of 10 and 15 is 30

2. 8 and 6

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72 …

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60….

Common multiples of 8 and 6 are 24, 48, …

LCM of 8 and 6 is 24

3. 4 and 10

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…..

Multiples of 10: 10, 20, 30, 40, 50, 60, …..

Common multiples of 4 and 10 are 20, 40, ….

LCM of 4 and 10 is 20

4. 6 and 16

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96

Multiples of 16: 16, 32, 48, 64, 80, 96

Common multiples of 6 and 16 are 48, 96…..

LCM of 6 and 16 is 48

Example

Find L.C.M of 8 and 12

L.C.M of 8, 12 = 2 × 2 × 2 × 3 = 24.

Multiply the common factors and other factors of two numbers to get its L.C.M

Do you Know?

If one number is a multiple of another number, then the bigger number is L.C.M and smaller number is H.C.F.

Example

L.C.M of 4, 16 is16

H.C.F of 4, 16 is 4

Think it: Can we say the highest common multiples for two numbers?