LCM( 32, 60, 84 ) = 3360
Step 1: Write down factorisation of each number:
32 = 2 · 2 · 2 · 2 · 2
60 = 2 · 2 · 3 · 5
84 = 2 · 2 · 3 · 7
Step 2 : Match primes vertically:
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||
84 | = | 2 | · | 2 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||||
84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 3360 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.