Question
Find Least Common Multiple of 594 and 594 using ladder method..
Answer
LCM( 594, 594 ) = 594
Explanation
Step 1 : Place the numbers inside division bar:
| 594 | 594 |
Step 2 : Find a prime number which divides both numbers.
In this example we can divide by 2. If any number is not divisible by 2 write it down unchanged.
| 2 | 594 | 594 |
| 297 | 297 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 594 | 594 |
| 3 | 297 | 297 |
| 99 | 99 |
| 2 | 594 | 594 |
| 3 | 297 | 297 |
| 3 | 99 | 99 |
| 33 | 33 |
| 2 | 594 | 594 |
| 3 | 297 | 297 |
| 3 | 99 | 99 |
| 3 | 33 | 33 |
| 11 | 11 |
| 2 | 594 | 594 |
| 3 | 297 | 297 |
| 3 | 99 | 99 |
| 3 | 33 | 33 |
| 11 | 11 | 11 |
| 1 | 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 = 594 · 594 = 594
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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