HCF and LCM are two of the most important concepts in mathematics. The full form of HCF is the Highest Common Factor and the full form of LCM is the Least Common Multiple. Both are fundamental to understanding the properties and relationships of numbers.
What is HCF ?
The Full form of HCF is Highest Common factor.
HCF is the highest number among all the common factors two or more numbers.
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HCF of two or more positive integers is the largest positive integer that divides each of the integers without leaving a remainder. HCF is also known as GCD (Greatest Common Divisor). For Example, HCF of 9 and 12 will be 3 because the highest number that divides both 9 and 12 is 4.
How to find HCF:-
1. Prime Factorization Method:
Step 1: Factorise each number into its prime factors.
Step 2: Identify the common prime factors.
Step 3: Product these common prime factors to get the HCF.
In short, HCF of two or more numbers = Product of the smallest power of each common prime factor, involved in the numbers.
Example:
2. Division method:
Step 1: Divide the larger number by the smaller number.
Step 2: Take the remainder and divide the previous divisor by this remainder.
Step 3: Repeat until the remainder is zero. The last non-zero remainder is the HCF.
What is LCM ?
The Full form of LCM is Least Common Multiple.
LCM is the smallest number among all the multiples of two or more numbers.
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The Least Common Multiple of two or more positive integers is the smallest or least positive integer that is divisible by each of the positive integers. For example, LCM of 9 and 12 is
Multiples of 9 are: 9, 18, 27, 36, 45, ….
Multiples of 12 are: 12, 24, 36, 48, ….
The common multiple of 9 and 12 are 36,72, 108,…. The least multiple number is 36. So, LCM of 9 and 12 is 36.
How to find LCM:-
1. Prime Factorization Method:
Step 1: Factorise each number into its prime factors.
Step 2: Identify the highest power of each prime factor present in the factorizations.
Step 3: Product these highest powers to get the LCM.
In short, LCM of two or more numbers = Product of the greatest power of each prime factor, involved in the numbers
2. Division method:
Step 1: List the numbers and divide by common prime factors until only 1s remain.
Step 2: Multiply all the divisors to get the LCM.
Important MCQs with Answers
