LCM( 1728, 423360 ) = 423360
Step 1 : Write the given numbers in a horizontal line.
1728 | 423360 |
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 | 1728 | 423360 |
864 | 211680 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 1728 | 423360 |
2 | 864 | 211680 |
2 | 432 | 105840 |
2 | 216 | 52920 |
2 | 108 | 26460 |
2 | 54 | 13230 |
3 | 27 | 6615 |
3 | 9 | 2205 |
3 | 3 | 735 |
5 | 1 | 245 |
7 | 1 | 49 |
7 | 1 | 7 |
1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1728, 423360 ) = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 7 · 7 = 423360 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.