LCM( 48, 60, 75 ) = 1200
Step 1: Write down factorisation of each number:
48 = 2 · 2 · 2 · 2 · 3
60 = 2 · 2 · 3 · 5
75 = 3 · 5 · 5
Step 2 : Match primes vertically:
48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||
75 | = | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||
75 | = | 3 | · | 5 | · | 5 | ||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | = | 1200 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.