LCM( 1650, 45, 1500 ) = 49500
Step 1 : Write the given numbers in a horizontal line.
1650 | 45 | 1500 |
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 | 1650 | 45 | 1500 |
825 | 45 | 750 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 1650 | 45 | 1500 |
2 | 825 | 45 | 750 |
3 | 825 | 45 | 375 |
3 | 275 | 15 | 125 |
5 | 275 | 5 | 125 |
5 | 55 | 1 | 25 |
5 | 11 | 1 | 5 |
11 | 11 | 1 | 1 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1650, 45, 1500 ) = 2 · 2 · 3 · 3 · 5 · 5 · 5 · 11 = 49500 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.