Greatest Common Multiple
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.
Another Example
Find the greatest common multiple of 30 and 40
Solution
Multiples of 30 are 30, 10, 6, 5, 3 and 1
Multiples of 40 are 40, 20, 10, 8, 5, 4, 2 and 1
10 is the highest common factor in both.
The greatest common multiple of 30 and 40 is 10
Practice Problem of Greatest Common Multiple
Find the greatest common multiple of 25 and 20
Find the greatest common multiple of 75 and 100
Find the greatest common multiple of 64 and 48
Find the greatest common multiple of 60 and 72
Find the greatest common multiple of 9 and 18
Answers
5
25
16
12
9
by: jeri
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