LCM( 513, 1134, 1215 ) = 323190
Step 1 : Write the given numbers in a horizontal line.
513 | 1134 | 1215 |
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 | 513 | 1134 | 1215 |
513 | 567 | 1215 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 513 | 1134 | 1215 |
3 | 513 | 567 | 1215 |
3 | 171 | 189 | 405 |
3 | 57 | 63 | 135 |
3 | 19 | 21 | 45 |
3 | 19 | 7 | 15 |
5 | 19 | 7 | 5 |
7 | 19 | 7 | 1 |
19 | 19 | 1 | 1 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 513, 1134, 1215 ) = 2 · 3 · 3 · 3 · 3 · 3 · 5 · 7 · 19 = 323190 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.