LCM( 8, 42, 84 ) = 168
Step 1: Write down factorisation of each number:
8 = 2 · 2 · 2
42 = 2 · 3 · 7
84 = 2 · 2 · 3 · 7
Step 2 : Match primes vertically:
8 | = | 2 | · | 2 | · | 2 | ||||
42 | = | 2 | · | 3 | · | 7 | ||||
84 | = | 2 | · | 2 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
8 | = | 2 | · | 2 | · | 2 | ||||||
42 | = | 2 | · | 3 | · | 7 | ||||||
84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 7 | = | 168 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.