 # To Find Lowest Common Multiple by using Division Method – Definition, Examples | How to find LCM by Short Division Method?

The least common multiple is the method to find the smallest common multiples of two or more numbers in the fractions. There are different methods to find the L.C.M of two or more numbers. Let us discuss how To Find Lowest Common Multiple by using Division Method. In addition to the steps, we also provide Examples to find Least Common Multiple three numbers by using Division Method.

To find the L.C.M of the numbers by division method we have to write the given numbers in a row by putting commas between the numbers and then divide the given number by prime numbers until you get 1 in the last row. The product of common and uncommon prime factors will become the Least or lowest common multiple of the numbers.

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## How to Find LCM by Division Method?

There are some steps to follow to find the lowest common multiples of the numbers by division method:
1. First write the numbers and separate the numbers by commas.
2. Now divide the given numbers with the smallest prime numbers like 2, 3, 5, 7, etc.
3. If any number is not divisible, then write the number in the next row.
4. Keep on dividing the row of numbers by prime numbers until we get the result as 1 in the last row.
5. Now multiply the common and non-common factors of all the prime numbers we obtained in the division method.
6. The product of the number will give the L.C.M of the numbers.

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### Finding LCM using Division Method Examples

Example 1.
Find least common multiple (L.C.M) of 20 and 60 by division method.
Solution:
Write your numbers in the top row.
Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.
Bring down any numbers that are not evenly divisible by the prime number.
Find the product of the prime numbers in the first column to get the L.C.M. LCM = 2 x 2 x 3 x 5
Thus the lowest common multiple of 20 and 60 = 60
Therefore, LCM(20, 60) = 60

Example 2.
Find least common multiple (L.C.M) of 2, 5 and 7 by division method.
Solution:
Write your numbers in the top row.
Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.
Bring down any numbers that are not evenly divisible by the prime number.
Find the product of the prime numbers in the first column to get the LCM LCM = 2 x 5 x 7
Thus the lowest common multiple of 2, 5, 7 = 70
Therefore, LCM(2, 5, 7) = 70

Example 3.
Find least common multiple (L.C.M) of 15 and 90 by division method.
Solution:
Write your numbers in the top row.
Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.
Bring down any numbers that are not evenly divisible by the prime number.
Find the product of the prime numbers in the first column to get the LCM LCM = 2 x 3 x 3 x 5
Thus the lowest common multiple of 15 and 90 = 90
Therefore, LCM(15, 90) = 90

Example 4.
Find least common multiple (L.C.M) of 12, 16 and 24 by division method.
Solution:
Write your numbers in the top row.
Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.
Bring down any numbers that are not evenly divisible by the prime number.
Find the product of the prime numbers in the first column to get the LCM LCM = 2 x 2 x 2 x 2 x 3
Thus the lowest common multiple of 12, 16, 24 = 48
Therefore, LCM(12, 16, 24) = 48

Example 5.
Find least common multiple (L.C.M) of 10 and 18 by division method.
Solution:
Write your numbers in the top row.
Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.
Bring down any numbers that are not evenly divisible by the prime number. Find the product of the prime numbers in the first column to get the LCM
LCM = 2 × 3 × 3 × 5
LCM = 90
lcm(10, 18) = 90
Thus the lowest common multiple of 10 and 18 is 90.

### FAQs on L.C.M by Division Method

1. How do you find the lowest common multiple?

To find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

2. What is the LCM of 3 and 4 by division method?

The Lowest Common Multiple of 3 and 4 is 12.

3. What is the LCM of the first 10 natural numbers?

LCM of the first 10 natural numbers is 2520.

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