LCM( 24, 48, 60 ) = 240
Step 1: Write down factorisation of each number:
24 = 2 · 2 · 2 · 3
48 = 2 · 2 · 2 · 2 · 3
60 = 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||
60 | = | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | = | 240 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.