LCM( 460, 480, 540 ) = 99360
Step 1 : Write the given numbers in a horizontal line.
460 | 480 | 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 | 460 | 480 | 540 |
230 | 240 | 270 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 460 | 480 | 540 |
2 | 230 | 240 | 270 |
2 | 115 | 120 | 135 |
2 | 115 | 60 | 135 |
2 | 115 | 30 | 135 |
3 | 115 | 15 | 135 |
3 | 115 | 5 | 45 |
3 | 115 | 5 | 15 |
5 | 115 | 5 | 5 |
23 | 23 | 1 | 1 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 460, 480, 540 ) = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 23 = 99360 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.