LCM( 95, 100, 105 ) = 39900
Step 1: Write down factorisation of each number:
95 = 5 · 19
100 = 2 · 2 · 5 · 5
105 = 3 · 5 · 7
Step 2 : Match primes vertically:
95 | = | 5 | · | 19 | ||||||||||
100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||
105 | = | 3 | · | 5 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
95 | = | 5 | · | 19 | ||||||||||||
100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||||
105 | = | 3 | · | 5 | · | 7 | ||||||||||
LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 7 | · | 19 | = | 39900 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.