Question
Find Least Common Multiple of 324, 756 and 972 using prime factorisation method.
Answer
LCM( 324, 756, 972 ) = 6804
Explanation
Step 1: Write down factorisation of each number:
324 = 2 · 2 · 3 · 3 · 3 · 3
756 = 2 · 2 · 3 · 3 · 3 · 7
972 = 2 · 2 · 3 · 3 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 324 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | ||||
| 756 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 7 | ||||
| 972 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 324 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | ||||||
| 756 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 7 | ||||||
| 972 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 3 | ||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 3 | · | 7 | = | 6804 |
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