Question
Find Least Common Multiple of 144, 180 and 200 using ladder method..
Answer
LCM( 144, 180, 200 ) = 3600
Explanation
Step 1 : Place the numbers inside division bar:
| 144 | 180 | 200 |
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 | 180 | 200 |
| 72 | 90 | 100 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 144 | 180 | 200 |
| 2 | 72 | 90 | 100 |
| 36 | 45 | 50 |
| 2 | 144 | 180 | 200 |
| 2 | 72 | 90 | 100 |
| 2 | 36 | 45 | 50 |
| 18 | 45 | 25 |
| 2 | 144 | 180 | 200 |
| 2 | 72 | 90 | 100 |
| 2 | 36 | 45 | 50 |
| 3 | 18 | 45 | 25 |
| 6 | 15 | 25 |
| 2 | 144 | 180 | 200 |
| 2 | 72 | 90 | 100 |
| 2 | 36 | 45 | 50 |
| 3 | 18 | 45 | 25 |
| 3 | 6 | 15 | 25 |
| 2 | 5 | 25 |
| 2 | 144 | 180 | 200 |
| 2 | 72 | 90 | 100 |
| 2 | 36 | 45 | 50 |
| 3 | 18 | 45 | 25 |
| 3 | 6 | 15 | 25 |
| 5 | 2 | 5 | 25 |
| 2 | 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 · 180 · 200 = 3600
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
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