Find Least Common Multiple of 100, 150 and 200 using ladder method..
Answer
LCM( 100, 150, 200 ) = 600
Explanation
Step 1 : Place the numbers inside division bar:
| 100 | 150 | 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 | 100 | 150 | 200 |
| 50 | 75 | 100 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 100 | 150 | 200 |
| 2 | 50 | 75 | 100 |
| 25 | 75 | 50 |
| 2 | 100 | 150 | 200 |
| 2 | 50 | 75 | 100 |
| 5 | 25 | 75 | 50 |
| 5 | 15 | 10 |
| 2 | 100 | 150 | 200 |
| 2 | 50 | 75 | 100 |
| 5 | 25 | 75 | 50 |
| 5 | 5 | 15 | 10 |
| 1 | 3 | 2 |
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 = 100 · 150 · 200 = 600
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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