LCM( 105, 135, 150 ) = 9450
Step 1: Write down factorisation of each number:
105 = 3 · 5 · 7
135 = 3 · 3 · 3 · 5
150 = 2 · 3 · 5 · 5
Step 2 : Match primes vertically:
105 | = | 3 | · | 5 | · | 7 | ||||||||
135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||
150 | = | 2 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
105 | = | 3 | · | 5 | · | 7 | ||||||||||
135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||||
150 | = | 2 | · | 3 | · | 5 | · | 5 | ||||||||
LCM | = | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | · | 7 | = | 9450 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.