LCM( 46, 78, 60 ) = 17940
Step 1 : Write the given numbers in a horizontal line.
46 | 78 | 60 |
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 | 46 | 78 | 60 |
23 | 39 | 30 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 46 | 78 | 60 |
2 | 23 | 39 | 30 |
3 | 23 | 39 | 15 |
5 | 23 | 13 | 5 |
13 | 23 | 13 | 1 |
23 | 23 | 1 | 1 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 46, 78, 60 ) = 2 · 2 · 3 · 5 · 13 · 23 = 17940 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.