LCM( 100, 3000 ) = 3000
Step 1: Write down factorisation of each number:
100 = 2 · 2 · 5 · 5
3000 = 2 · 2 · 2 · 3 · 5 · 5 · 5
Step 2 : Match primes vertically:
100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||
3000 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||||
3000 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 5 | ||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 5 | = | 3000 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.