Find Least Common Multiple of 20, 60 and 180 using prime factorisation method.
Answer
LCM( 20, 60, 180 ) = 180
Explanation
Step 1: Write down factorisation of each number:
20 = 2 · 2 · 5
60 = 2 · 2 · 3 · 5
180 = 2 · 2 · 3 · 3 · 5
Step 2 : Match primes vertically:
| 20 | = | 2 | · | 2 | · | 5 | ||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||
| 180 | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 20 | = | 2 | · | 2 | · | 5 | ||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||
| 180 | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | ||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 180 |
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