Question
Find Least Common Multiple of 300, 528 and 690 using ladder method..
Answer
LCM( 300, 528, 690 ) = 303600
Explanation
Step 1 : Place the numbers inside division bar:
| 300 | 528 | 690 |
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 | 300 | 528 | 690 |
| 150 | 264 | 345 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 300 | 528 | 690 |
| 2 | 150 | 264 | 345 |
| 75 | 132 | 345 |
| 2 | 300 | 528 | 690 |
| 2 | 150 | 264 | 345 |
| 3 | 75 | 132 | 345 |
| 25 | 44 | 115 |
| 2 | 300 | 528 | 690 |
| 2 | 150 | 264 | 345 |
| 3 | 75 | 132 | 345 |
| 5 | 25 | 44 | 115 |
| 5 | 44 | 23 |
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 = 300 · 528 · 690 = 303600
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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