Find Least Common Multiple of 120, 150 and 135 using prime factorisation method.
Answer
LCM( 120, 150, 135 ) = 5400
Explanation
Step 1: Write down factorisation of each number:
120 = 2 · 2 · 2 · 3 · 5
150 = 2 · 3 · 5 · 5
135 = 3 · 3 · 3 · 5
Step 2 : Match primes vertically:
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||
| 150 | = | 2 | · | 3 | · | 5 | · | 5 | ||||||||
| 135 | = | 3 | · | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||||
| 150 | = | 2 | · | 3 | · | 5 | · | 5 | ||||||||||
| 135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | = | 5400 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
This page was created using
LCM Calculator