LCM( 1080, 720, 1560 ) = 28080
Step 1 : Write the given numbers in a horizontal line.
1080 | 720 | 1560 |
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 | 1080 | 720 | 1560 |
540 | 360 | 780 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 1080 | 720 | 1560 |
2 | 540 | 360 | 780 |
2 | 270 | 180 | 390 |
2 | 135 | 90 | 195 |
3 | 135 | 45 | 195 |
3 | 45 | 15 | 65 |
3 | 15 | 5 | 65 |
5 | 5 | 5 | 65 |
13 | 1 | 1 | 13 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1080, 720, 1560 ) = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 13 = 28080 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.