LCM( 180, 216, 324 ) = 3240
Step 1 : Write the given numbers in a horizontal line.
180 | 216 | 324 |
Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 2.
(if any number is not divisible by 2, write it down unchanged)
2 | 180 | 216 | 324 |
90 | 108 | 162 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 180 | 216 | 324 |
2 | 90 | 108 | 162 |
2 | 45 | 54 | 81 |
3 | 45 | 27 | 81 |
3 | 15 | 9 | 27 |
3 | 5 | 3 | 9 |
3 | 5 | 1 | 3 |
5 | 5 | 1 | 1 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 180, 216, 324 ) = 2 · 2 · 2 · 3 · 3 · 3 · 3 · 5 = 3240 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.