LCM( 180, 384, 432 ) = 17280
Step 1 : Write the given numbers in a horizontal line.
180 | 384 | 432 |
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 | 384 | 432 |
90 | 192 | 216 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 180 | 384 | 432 |
2 | 90 | 192 | 216 |
2 | 45 | 96 | 108 |
2 | 45 | 48 | 54 |
2 | 45 | 24 | 27 |
2 | 45 | 12 | 27 |
2 | 45 | 6 | 27 |
3 | 45 | 3 | 27 |
3 | 15 | 1 | 9 |
3 | 5 | 1 | 3 |
5 | 5 | 1 | 1 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 180, 384, 432 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 = 17280 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.