**Lowest common multiple :**

The smallest among the common multiples of two numbers is called their least common multiple (LCM).

We can find L.C.M in two different methods

(i) Common multiple method to find lcm

(ii) Factorization method to find lcm

(iii) Using ladder method to find lcm

Now let us see the above methods one by one.

We have to follow the steps given below, when we use common multiple method to find the L.C.M of two or more numbers.

**Step 1 :**

List the multiples of the given numbers

**Step 2 :**

Circle and write the common multiples

**Step 3 :**

The smallest common multiple of is L.C.M.

**Example 1 :**

Find the L.C.M of 16 and 24 using common multiple method.

**Solution : **

Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, .........

Multiples of 24 = 24, 48, 72, 96, 120, 144, 168,.............

The smallest multiple among the common multiples is the L.C.M

Hence the L.C.M of 16 and 24 is 48.

We have to follow the steps given below, when we use factorization method to find the L.C.M of two or more numbers.

**Step 1 :**

Find the prime factors of the given numbers.

**Step 2 :**

Circle the common factors.

**Step 3 :**

Find the product of the common factors.Multiply this product with independent factors.

**Example 2 :**

Find the L.C.M of 16 and 24 using factorization method.

**Solution : **

Multiples of 16 = 2 x 2 x 2 x 2

Multiples of 24 = 2 x 2 x 3 x 2

By multiplying the common factors with independent factors, we get

= 2 x 2 x 2 x 3 x 2 = 48

Hence the L.C.M of 16 and 24 is 48.

We use the steps given below to do prime factorization using ladder diagram.

**Step 1 : **

Put the given numbers inside the "L" shape

**Step 2 :**

We have to split the given number by prime numbers only. That is, always we have to put prime numbers out side the "L" shape.

Given below will be helpful to find the prime number which exactly divides the given number.

- A number which ends with 0, 2, 4, 6 and 8 is divisible by the smallest prime number 2.
- A number which ends with 0 or 5 is divisible by 5
- If the sum of digits of the given number is a multiple of 3, then the given number is divisible by 3.

**Step 4 :**

Repeat this process until get prime numbers inside the ladder.

**Step 5 :**

The product of numbers inside and out side the ladder will be the L.C.M

**Example 3 :**

Find the L.C.M of 16 and 24 using ladder diagram

**Solution : **

L.C.M of 16 and 24 = 2 x 2 x 2 x 2 x 3

= 48

After having gone through the stuff given above, we hope that the students would have understood "Lowest common multiple".

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