LCM( 14, 16, 18 ) = 1008
Step 1: Write down factorisation of each number:
14 = 2 · 7
16 = 2 · 2 · 2 · 2
18 = 2 · 3 · 3
Step 2 : Match primes vertically:
14 | = | 2 | · | 7 | ||||||||||
16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
18 | = | 2 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
14 | = | 2 | · | 7 | ||||||||||||
16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
18 | = | 2 | · | 3 | · | 3 | ||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | = | 1008 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.