Factorization Method of LCM and HCF

Factorization Method of LCM and HCF is one of the most important concepts in mathematics. Factorization is the process of finding the factors of a number. Factors of a number are those numbers that divide into it exactly. For example: Maria bought 20 soft toys online to give away as return gift to kids on her daughter’s birthday. In order to find the factors of the number 20 soft toys online , we need to divide the number with prime numbers. 20 = 2 * 2* 5. Therefore, 2, 2 and 5 are the factors of 20. A factor that is a prime number is called a prime factor.

Common Factors: LCM and HCF
When we divide two numbers and find common factors that are divisor of each number, these are termed as common factors. For example: Lily bought 6 wooden baby toys and Heema bought 8 wooden baby toys online. Here, finding common factors of 6 and 8, we get: 6 = 2 * 3 and 8 = 2 * 2 * 2.  2 is the common factor of 6 and 8.

Highest Common Factor (HCF)
The Highest Common Factor of two or more numbers is called the highest common factor. It is also referred as Greatest Common Factor (GCF). For example: Harry bought 60 kids’ toy collection boxes online and Mahesh bought 70 kids toy collection  boxes online. Find the HCF of 60 and 70:
60 = 2 * 2 * 3 * 5
70 = 2 * 5 * 7
The common factors of 60 and 70 are 2 and 5.
The HCF of 60 and 70 is: 2 * 3 * 5 * 7 = 210

Lowest Common Multiple (LCM)
The Least Common Factor of two or more numbers is the lowest multiple of a number. For example: Manish bought 18 apples and 24 mangoes from the market. Find the LCM of 18 and 24:
18 = 18, 36, 54, 72, 90, 108, 126 etc
24 = 24, 48, 72, 96, 120 etc
The LCM of 18 and 24 is 72.
This is the factorization method of LCM and HCF.