Question
Find Least Common Multiple of 144, 252 and 630 using ladder method..
Answer
LCM( 144, 252, 630 ) = 5040
Explanation
Step 1 : Place the numbers inside division bar:
| 144 | 252 | 630 |
Step 2 : Find a prime number which can divide at least two of your numbers.
In this example we can divide by 2. If any number is not divisible by 2 write it down unchanged.
| 2 | 144 | 252 | 630 |
| 72 | 126 | 315 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 144 | 252 | 630 |
| 2 | 72 | 126 | 315 |
| 36 | 63 | 315 |
| 2 | 144 | 252 | 630 |
| 2 | 72 | 126 | 315 |
| 3 | 36 | 63 | 315 |
| 12 | 21 | 105 |
| 2 | 144 | 252 | 630 |
| 2 | 72 | 126 | 315 |
| 3 | 36 | 63 | 315 |
| 3 | 12 | 21 | 105 |
| 4 | 7 | 35 |
| 2 | 144 | 252 | 630 |
| 2 | 72 | 126 | 315 |
| 3 | 36 | 63 | 315 |
| 3 | 12 | 21 | 105 |
| 7 | 4 | 7 | 35 |
| 4 | 1 | 5 |
Since there are no primes that divides at least two of given numbers, we conclude that the LCM is a product of starting numbers.
LCM = 144 · 252 · 630 = 5040
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
This page was created using
LCM Calculator