LCM( 360, 420, 540 ) = 7560
Step 1 : Write the given numbers in a horizontal line.
360 | 420 | 540 |
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 | 360 | 420 | 540 |
180 | 210 | 270 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 360 | 420 | 540 |
2 | 180 | 210 | 270 |
2 | 90 | 105 | 135 |
3 | 45 | 105 | 135 |
3 | 15 | 35 | 45 |
3 | 5 | 35 | 15 |
5 | 5 | 35 | 5 |
7 | 1 | 7 | 1 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 360, 420, 540 ) = 2 · 2 · 2 · 3 · 3 · 3 · 5 · 7 = 7560 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.