Question
Find Least Common Multiple of 567 and 729 using ladder method..
Answer
LCM( 567, 729 ) = 5103
Explanation
Step 1 : Place the numbers inside division bar:
| 567 | 729 |
Step 2 : Find a prime number which divides both numbers.
In this example we can divide by 3. If any number is not divisible by 3 write it down unchanged.
| 3 | 567 | 729 |
| 189 | 243 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 3 | 567 | 729 |
| 3 | 189 | 243 |
| 63 | 81 |
| 3 | 567 | 729 |
| 3 | 189 | 243 |
| 3 | 63 | 81 |
| 21 | 27 |
| 3 | 567 | 729 |
| 3 | 189 | 243 |
| 3 | 63 | 81 |
| 3 | 21 | 27 |
| 7 | 9 |
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 = 567 · 729 = 5103
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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