Find Least Common Multiple of 150, 360 and 900 using ladder method..
Answer
LCM( 150, 360, 900 ) = 1800
Explanation
Step 1 : Place the numbers inside division bar:
| 150 | 360 | 900 |
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 | 150 | 360 | 900 |
| 75 | 180 | 450 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 150 | 360 | 900 |
| 2 | 75 | 180 | 450 |
| 75 | 90 | 225 |
| 2 | 150 | 360 | 900 |
| 2 | 75 | 180 | 450 |
| 3 | 75 | 90 | 225 |
| 25 | 30 | 75 |
| 2 | 150 | 360 | 900 |
| 2 | 75 | 180 | 450 |
| 3 | 75 | 90 | 225 |
| 3 | 25 | 30 | 75 |
| 25 | 10 | 25 |
| 2 | 150 | 360 | 900 |
| 2 | 75 | 180 | 450 |
| 3 | 75 | 90 | 225 |
| 3 | 25 | 30 | 75 |
| 5 | 25 | 10 | 25 |
| 5 | 2 | 5 |
| 2 | 150 | 360 | 900 |
| 2 | 75 | 180 | 450 |
| 3 | 75 | 90 | 225 |
| 3 | 25 | 30 | 75 |
| 5 | 25 | 10 | 25 |
| 5 | 5 | 2 | 5 |
| 1 | 2 | 1 |
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 = 150 · 360 · 900 = 1800
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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