LCM( 284, 213, 142 ) = 852
Step 1: Write down factorisation of each number:
284 = 2 · 2 · 71
213 = 3 · 71
142 = 2 · 71
Step 2 : Match primes vertically:
284 | = | 2 | · | 2 | · | 71 | ||
213 | = | 3 | · | 71 | ||||
142 | = | 2 | · | 71 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
284 | = | 2 | · | 2 | · | 71 | ||||
213 | = | 3 | · | 71 | ||||||
142 | = | 2 | · | 71 | ||||||
LCM | = | 2 | · | 2 | · | 3 | · | 71 | = | 852 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.