The least common many (L.C.M.) of 2 or much more numbers is the the smallest number which have the right to be exactly divided by every of the offered number.

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**Let us find the L.C.M. Of 2, 3 and also 4.**

**Multiples the 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, ...... Etc. **

**Multiples that 3 space 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...... Etc.**

**Multiples that 4 room 4, 8, 12, 16, 20, 24, 28, 32, 36, ...... Etc.**

**Common multiples the 2, 3 and 4 space 12, 24, 36, ...... Etc.**

**Therefore, the smallest usual multiple or least common multiples the 2, 3 and also 4 is 12.**

We recognize that the lowest typical multiple or LCM of two ormore number is the the smallest of all typical multiples.

Let us take into consideration the number 28 and 12

Multiples of 28 are 28, 56, 84, 112, …….

Multiples of 12 room 12, 24, 36, 48, 60, 72, 84, …….

The lowest typical multiple (LCM) that 28 and 12 is 84.

Let us think about the very first six multiples of 4 and also 6.

The an initial six multiples the 4 are 4, 8, 12, 16, 20, 24

The an initial six multiples the 6 are 6, 12,18, 24, 30, 36

The numbers 12 and 24 room the first two usual multiples of4 and also 6. In the over example the least usual multiple that 4 and 6 is 12.

Hence, the least common multiple or LCM is the smallestcommon multiple of the provided numbers.

**Consider the following.**

**(i) 12 is the least usual multiple (L.C.M) the 3 and 4.**

**(ii) 6 is the least usual multiple (L.C.M) of 2, 3 and 6. **

**(iii) 10 is the least typical multiple (L.C.M) of 2 and also 5. **

**We can likewise find the L.C.M. Of given numbers through their finish factorisation.**

**To find for instance, L.C.M. That 24, 36 and 40, we first factorise castle completely.**

**24 = 2 × 2 × 2 × 3 = 2(^3) × 3(^1)**

**36 = 2 × 2 × 3 × 3 = 2(^2) × 3(^2)**

**40 = 2 × 2 × 2 × 5 = 2(^3) × 5(^1)**

**L.C.M. Is the product of greatest power that primes existing in the factors.**

**Therefore, L.C.M. The 24, 36 and 40 = 2(^3) × 3(^2) × 5(^1) = 8 × 9 × 5 = 360**

Solved instances to find the lowest typical multiple or the least typical multiple:

1. Uncover the L.C.M. That 8, 12, 16, 24 and 36

8 = 2 × 2 × 2 = 2(^3)

12 = 2 × 2 × 3 = 2(^2) × 3(^1)

16 = 2 × 2 × 2 × 2 = 2(^4)

24 = 2 × 2 × 2 × 3 = 2(^3) × 3(^1)

36 = 2 × 2 × 3 × 3 = 2(^2) × 3(^2)

Therefore, L.C.M. That 8, 12, 16, 24 and also 36 = 2(^4) × 3(^2) = 144.

**2. Find the LCM the 3, 4 and 6 by listing the multiples.**

**Solution:**

The multiple of 3 are 3, 6, 12, 15, 18, 21, 24

The lot of of 4 are 4, 8, 12, 16, 20, 24, 28

The lot of of 6 are 6, 12, 18, 24, 30, 36, 42

The usual multiples that 3, 4 and 6 are 12 and also 24

So, the least typical multiple the 3, 4 and 6 is 12.

We can find LCM of offered numbers by listing multiples or bylong division method.

**2. Uncover the LCM of 18, 36 and 72 by department method.**

**Solution:**

Write the numbers in a heat separated through commas. Division thenumbers by a typical prime number. We stop separating after reaching the primenumber. Uncover the product the divisors and also the remainders.

**● ****Multiples.**

**Common Multiples.****Least usual Multiple (L.C.M).****To uncover Least common Multiple by utilizing Prime factorization Method.****Examples to discover Least usual Multiple by utilizing Prime factorization Method.**

**To find Lowest typical Multiple by using department Method**

**Examples to uncover Least common Multiple of 2 numbers through using division Method****Examples to discover Least usual Multiple of 3 numbers by using department Method**

**Relationship in between H.C.F. And L.C.M.**

**Worksheet on H.C.F. And also L.C.M.**

**Word difficulties on H.C.F. And L.C.M.**

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