How to Find LCM By Using Prime Factorization Method?

LCM of numbers can be determined using various methods. There are 3 methods to calculate the least common multiple of two or more numbers. By prime factorization method, by division method, by the listing method.in this article how to find LCM by using prime factorization.

How to find LCM by using the prime factorization method?

By using the prime factorization method we can determine the LCM of the given numbers. To find the LCM of two numbers using the prime factorization method, we use the steps given below:

Step 1: calculate the prime factors of the given numbers by the repeated division method.

Step2: Write the numbers in their power form. Find the product of only those prime factors that have the greatest power.

Step 3: The product of these factors with the greatest powers is the LCM of the given numbers.

Let us learn this method using the example given below

For example: Find the least common multiple (LCM) of 24 and 36using prime factorization.

Solution:

Let us find the LCM of 24 and 36 using the prime factorization method.

Step1: The prime factorization of 24 and 36 are:

24=2x2x2x3

36=2x2x3x3

Step 2: If we write these prime factors in their exponent form it will be expressed as,

24=2³X3

36=2²x3²

Step3: Now, we will calculate the product of only those factors that have the greatest powers among these. This will be,

2³X3²=8×9=72

Therefore LCM Of 24 and 36=72

For example: to find the LCM of 336 and 54 by using prim factorization

Solution: Let us find the LCM of 336and 54 using the prime factorization method.

Step1: The prime factorization of 336 and 54 are:

336=2x2x2x2x3x7

54=2x3x3x3x1

Step 2: If we write these prime factors in their exponent form it will be expressed as,

336=2⁴x3¹x7¹

54=2¹x3³x1

54=2¹x3³x7⁰          x⁰=1

Step3: Now, we will calculate the product of only those factors that have the greatest powers among these. This will be,

2⁴x3³x7¹=16x27x7=3024

Therefore LCM Of 336 and 54=3024