How to Find LCM and HCF ?

How to Calculate Least Common Multiple (LCM) and Highest Common Factor (HCF)?

Highest Common Factor and Least Common Multiple Calculation

The least common multiple is the smallest positive integer which is multiple of two or more numbers. It is denoted by LCM. It is also called as smallest/lowest common multiple.
The largest common factor of two or more numbers is called as highest common factor. It is denoted by HCF. It is also known as GCF (Greatest Common Factor) or GCD (Greatest Common Divisor). Learn here how to find LCM and HCF with simple steps.

Example to Find LCM :
Let us consider an example,
Find LCM of 15 and 24.
Step 1: Find the prime factors of these two numbers.
Prime Factors of 15 = 3 x 5
Prime Factors of 24 = 2 x 2 x 2 x 3

Step 2: Identify the most repeated numbers in prime factorization.
Prime Factors of 15 = 3x5
Prime Factors of 24 = 2x2x2x 3
The number 3 appears once in prime factorization of 15 and 24. So, let us take one 3 in common for both 15 and 24.
The number 2 appears thrice in prime factorization of 24. So, all three 2 is considered.
And the number 5 appears once in prime factorization of 15.

Step 3: Multiply all the numbers which is in bold font style,
The product is,
3x5x2x2x2 = 15 x 8 = 120
So the LCM of 15 and 24 is 120

Example to Find HCF :
HCF of 12 and 18.
Step 1: Find the prime factors of these two numbers
Prime factors of 12 = 2 x 2 x 3
Prime factors of 18 = 2 x 3 x 3

Step 2: Identify the common factors of 12 and 18
2 and 3 are the common factors of 12 and 18.

Step 3: Identify the highest factor among the common factors.
Here 3 is the highest common factor.

Learn to find least common multiple of numbers using GCD with our how to calculate LCM tutorial.

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