The LCM or least common multiple is another number which is useful in solving many math problems. To find the LCM of two numbers, It is important to check whether the denominators of the two numbers are common or uncommon. Letâ€™s find out how to find the LCM of two numbers with the same or different denominators and also, the LCM of fractions.

## How to Find LCM of Two Numbers?

To find the LCM of two numbers 30 and 45. Out of other ways, One way to find the LCM of two numbers is as follows:

*Step 1:* To first list the **prime factors** of each number.

30 = 2 Ã— 3 Ã— 5

45 = 3 Ã— 3 Ã— 5

*Step 2:* Next multiply each factor the **maximum number of times** it occurs in either number.

If the same factor occurs more than once in both numbers, then multiply the factor the maximum number of times it occurs.

The occurrence of Numbers in the above example:

**2**: one time

**3**: two times

**5**: one times

LCM = 2 Ã— 3 Ã— 3 Ã— 5 = 90

After calculating the LCM, always check to be sure your answer can be divided evenly by both numbers.

## Examples of LCM of two numbers

**Example 1**: Find the L.C.M of 18 and 24 by using the division method?

Solution:

For numbers 18 and 24 = 2 Ã— 2 Ã— 3 Ã— 2 = 24 is the LCM.

**Example 2**: Find the Least Common Multiples of these sets of numbers – 3, 9, 21

Solution:

*Step 1*: List the **prime factors** of each.

3: 3

9: 3 Ã— 3

21: 3 Ã— 7

Step 2: Multiply each factor the **maximum number of times** it occurs in any of the numbers.

The occurrence of Numbers in the above example:

3: two times

7: one time

3 x 3 x 7 = 63

9 has two 3s, and 21 has one 7, so we multiply 3 two times, and 7 once.

This gives us 63, the lowest number that can be divided evenly by 3, 9, and 21.

**Example 3:** Find the Least common factor of 12, 80.

**Solution: **

*Step 1*: List the prime factors of each.

12: 2 Ã— 2 Ã— 3

80: 2 Ã— 2 Ã— 2 Ã— 2 Ã— 5

*Step 2:*

Multiply each factor the maximum number of times it occurs in either number.

*Step 3:*

The occurrence of Numbers in the above example:

2: 4 times

3: 1 time

5: 1 time

2 x 2 x 2 x 2 x 3 x 5 =240

12 has one 3, and 80 has four 2’s and one 5, so we multiply 2 four times, 3 once, and five once.

This gives us 240, the lowest number that can be divided by both 12 and 80.

## How to Find LCM of Fractions?

Formula to find the LCM of two fractions is:

L.C.M = \(\frac{LCM of the numerators}{HCF of denominators}\) |

*Step 1:* If the two fractions are :

*Step 2*: LCM of two numbers is the lowest/smallest number which is a multiple of both.

HCF of two numbers is the largest/maximum whole number which is a factor of both.

*Step 3*: Letâ€™s learn it using an example:

LCM of â…˜ Â and 3/7

LCM of the numbers, \(\frac{4}{3}\) / \(\frac{5}{7}\) = LCM

12/1 = 12

HCF of the numbers, \(\frac{4}{3}\)/\(\frac{5}{7}\) = HCF

1/35

L.C.M = LCM of the numerators/HCF of denominators

L.C.M = \(\frac{12}{1/35}\)

L.C.M = 12 x 35 = 420.

Note: We must know how to find both HCF and LCM for this.

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Properties of HCF and LCM | Prime factorization and Division method for HCF and LCM |