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

__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**,

**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?

Tags : Numbers | Term 2 Chapter 2 | 5th Maths , 5th Maths : Term 2 Unit 2 : Numbers

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5th Maths : Term 2 Unit 2 : Numbers : Least Common Multiple (L.C.M ) | Numbers | Term 2 Chapter 2 | 5th Maths

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