LCM( 15, 12, 8 ) = 120
Step 1: Write down factorisation of each number:
15 = 3 · 5
12 = 2 · 2 · 3
8 = 2 · 2 · 2
Step 2 : Match primes vertically:
15 | = | 3 | · | 5 | ||||||
12 | = | 2 | · | 2 | · | 3 | ||||
8 | = | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
15 | = | 3 | · | 5 | ||||||||
12 | = | 2 | · | 2 | · | 3 | ||||||
8 | = | 2 | · | 2 | · | 2 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | = | 120 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.