In Mathematics, we have learned different concepts in our primary and secondary classes. All the concepts which we have learned are equally important. LCM and HCF are the two different concepts in Maths, and it has many applications in our day to day activities. For example, LCM is used to interpret that something will occur again at the same time.
As we know, the digits are the unique characters (i.e., 0, 1, 5, 7, and so on). The unique characters can be used alone or in the group (such as 35, 68, etc.). The numerical digit is called “Number”. There are different types of numbers. Each type of number has its properties, which differs from each other. Here, we will discuss what is LCM and HCF and the methods to find the LCM and HCF. Also, learn what kind of number is used in finding the LCM and HCF of the numbers.
What is LCM?
LCM means Least Common Multiple. In Maths, “multiples” means a number divided by the given number, in which the remainder should be zero. For example, 15 is a multiple of 5.
The LCM of two numbers is the smallest non-zero number, which is the multiple of both the numbers.
For example, LCM of 2, and 3 is 6
Here, both 2 and 3 do not have any prime factor in common.
The multiples of 2 are 2, 4, 6, 8, 10, 12, …
The multiples of 3 are 3, 6, 9, 12, 15, …
Here, the least common multiple of 2 and 3 is 6.
What is HCF?
HCF means Highest Common Factor. HCF is also called GCD (Greatest Common Divisor). HCF of two numbers is the largest possible number, that divides both the numbers exactly. For example, GCD of 9 and 12 is 3.
The factors of 9 are 1, 3 and 9.
The factors of 12 are 1, 2, 3, 4, 6, and 12
Here, the greatest factor that divides 9 and 12 exactly, and common in both the numbers is 3.
Both LCM and HCF of the numbers can be found using different methods. They are:
- Prime Factorization Method
- Long Division Method
Here, let us discuss the prime factorization method to find the LCM and HCF of the two or more numbers.
Finding LCM and HCF using Prime Factorization Method
Prime factorization method is the process of finding the factors of the given number in terms of its prime numbers. In this method, the prime factors of a number can be found by keep on dividing the original number by the smallest prime factors, until we get the remainder 1.
LCM of 12 and 15
The prime factors of 12 are 2 × 2 × 3
The prime factors of 15 are 3 × 5
Here, LCM of 12 and 15 is 2 × 2 × 3 × 5
Hence, LCM (12, 15) is 60
Similarly, if we want to find the HCF of 12 and 15, the greatest common factor that is common in both the numbers is 3.
Hence, HCF (12, 15) is 3.
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