Find Least Common Multiple of 5184, 2592 and 1728 using prime factorisation method.
Answer
LCM( 5184, 2592, 1728 ) = 5184
Explanation
Step 1: Write down factorisation of each number:
5184 = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 3
2592 = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 3
1728 = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 5184 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 |
| 2592 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | ||
| 1728 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 5184 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | ||
| 2592 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | ||||
| 1728 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | = | 5184 |
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