LCM( 66, 78, 100 ) = 42900
Step 1: Write down factorisation of each number:
66 = 2 · 3 · 11
78 = 2 · 3 · 13
100 = 2 · 2 · 5 · 5
Step 2 : Match primes vertically:
66 | = | 2 | · | 3 | · | 11 | ||||||||
78 | = | 2 | · | 3 | · | 13 | ||||||||
100 | = | 2 | · | 2 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
66 | = | 2 | · | 3 | · | 11 | ||||||||||
78 | = | 2 | · | 3 | · | 13 | ||||||||||
100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||||
LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 11 | · | 13 | = | 42900 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.