LCM( 30, 32, 40 ) = 480
Step 1: Write down factorisation of each number:
30 = 2 · 3 · 5
32 = 2 · 2 · 2 · 2 · 2
40 = 2 · 2 · 2 · 5
Step 2 : Match primes vertically:
30 | = | 2 | · | 3 | · | 5 | ||||||||
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||
40 | = | 2 | · | 2 | · | 2 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
30 | = | 2 | · | 3 | · | 5 | ||||||||||
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | = | 480 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.