LCM( 240, 318, 426 ) = 903120
Step 1: Write down factorisation of each number:
240 = 2 · 2 · 2 · 2 · 3 · 5
318 = 2 · 3 · 53
426 = 2 · 3 · 71
Step 2 : Match primes vertically:
240 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||
318 | = | 2 | · | 3 | · | 53 | ||||||||||
426 | = | 2 | · | 3 | · | 71 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
240 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||
318 | = | 2 | · | 3 | · | 53 | ||||||||||||
426 | = | 2 | · | 3 | · | 71 | ||||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 53 | · | 71 | = | 903120 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.