How to Find LCM by using the Division Method?

The least common multiple (LCM) of numbers can be determined using a different method. There are three methods to calculate the least common multiple of two numbers.

• Least common multiple (LCM) by Listing Method
• Least common multiple (LCM) by prime factorization method
• Least common multiple (LCM) by division method

In This article how to find LCM by using the division Method.

How to find LCM by using the division Method?

In order to determine the LCM by the division method, we divide the numbers by a common prime number, and these prime factors are used to find the LCM of those numbers. Let us learn this method using the steps given below:

Step 1: calculate a prime number that is a factor of at least one of the given numbers.  The prime number writes this on the left of the given numbers.

Step 2:if the prime number in step 1 is a factor of the number, then divide the number by the prime and write the quotient below it. If the prime number in step 1 is not a factor of the number, then the number write in the row below as it is. Continue the process until 1 is left in the last row.

Let us understand this method using the example given below.

Example: calculate the least common multiple (LCM) of 8 and 15 using the division method.

Solution: Let us calculate the least common multiple (LCM) of 8 and 15 using the division method using the steps given below.

Step 1: 2 is the smallest prime number and it is a factor of 8. Write 2 on the left of the two numbers. For each number in the right column, continue calculating out prime numbers which are their factors.

Step 2: 2 divides 8 but it is not a factor of 15, so we write the number 15 in the row below as it is. Continue the process until 1 is left in the last row. Then, we divide 3 and 15 by 3. This gives us 1 and 3. Now, again we write 5 on the left side and we finally get 1, 1 as the quotient in the last row.

Step 3: Then we multiply these numbers on the left. The Least Common Multiple (LCM) is the product of all these prime numbers.

LCM of 8 and 15 is;2x2x2x3x5=120

Though we have three various methods to calculate the least common multiple, the division method is the most common and easy method that we use.