LCM( 32, 18, 100 ) = 7200
Step 1: Write down factorisation of each number:
32 = 2 · 2 · 2 · 2 · 2
18 = 2 · 3 · 3
100 = 2 · 2 · 5 · 5
Step 2 : Match primes vertically:
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
18 | = | 2 | · | 3 | · | 3 | ||||||||||||
100 | = | 2 | · | 2 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||||
18 | = | 2 | · | 3 | · | 3 | ||||||||||||||
100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | = | 7200 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.