LCM( 318, 400, 226 ) = 7186800
Step 1: Write down factorisation of each number:
318 = 2 · 3 · 53
400 = 2 · 2 · 2 · 2 · 5 · 5
226 = 2 · 113
Step 2 : Match primes vertically:
318 | = | 2 | · | 3 | · | 53 | ||||||||||||
400 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 5 | ||||||
226 | = | 2 | · | 113 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
318 | = | 2 | · | 3 | · | 53 | ||||||||||||||
400 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 5 | ||||||||
226 | = | 2 | · | 113 | ||||||||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 53 | · | 113 | = | 7186800 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.