LCM( 12, 14, 16 ) = 336
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
14 = 2 · 7
16 = 2 · 2 · 2 · 2
Step 2 : Match primes vertically:
12 | = | 2 | · | 2 | · | 3 | ||||||
14 | = | 2 | · | 7 | ||||||||
16 | = | 2 | · | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
12 | = | 2 | · | 2 | · | 3 | ||||||||
14 | = | 2 | · | 7 | ||||||||||
16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 7 | = | 336 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.