LCM( 24, 60, 120 ) = 120
Step 1: Write down factorisation of each number:
24 = 2 · 2 · 2 · 3
60 = 2 · 2 · 3 · 5
120 = 2 · 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
24 | = | 2 | · | 2 | · | 2 | · | 3 | ||
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||
120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||
120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||
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.