subject: Greatest Common Multiple [print this page] Introduction about greatest common multiple
Greatest common multiple is the highest common multiple of two or more numbers. Greatest common multiple can also be expressed as greatest common factor. This can be abbreviated as GCF or HCF. To find the greatest common multiple we use two methods. The first method is by finding the common highest factor that divides both the number and another r method is by using the prime factorization.
Greatest Common Multiple - Definition
When we list out the factors of two or more numbers, we may find many common multiples of all the numbers. The highest multiple among them is called as greatest common multiple
Here we can work on an example by both the method of finding greatest common multiple.
For example, find the greatest common multiple of 20 and 30.
Method I
The factors of 32 are 32, 16, 8, 4, 2 and1.
The factors of 48 are 48, 24, 16, 12, 8, 6, 4, 3, 2and1.
Here the common multiples of 32 and 48 are 16, 8, 4, 2 and 1. Among these multiples the greatest common multiple is 16.
Method II
By using prime factorization
Prime factors of 32 are 2x2x2x2x2
Prime factors of 48 are 2x2x2x2x3
The factors 2x2x2x2 appear common in both. When multiplying this we get 16 which is the greatest common multiple.
