LCM( 18, 34, 32 ) = 4896
Step 1: Write down factorisation of each number:
18 = 2 · 3 · 3
34 = 2 · 17
32 = 2 · 2 · 2 · 2 · 2
Step 2 : Match primes vertically:
18 | = | 2 | · | 3 | · | 3 | ||||||||||
34 | = | 2 | · | 17 | ||||||||||||
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
18 | = | 2 | · | 3 | · | 3 | ||||||||||||
34 | = | 2 | · | 17 | ||||||||||||||
32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 17 | = | 4896 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.