Question
Find Least Common Multiple of 36, 54 and 96 using ladder method..
Answer
LCM( 36, 54, 96 ) = 864
Explanation
Step 1 : Place the numbers inside division bar:
| 36 | 54 | 96 |
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 | 36 | 54 | 96 |
| 18 | 27 | 48 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 36 | 54 | 96 |
| 2 | 18 | 27 | 48 |
| 9 | 27 | 24 |
| 2 | 36 | 54 | 96 |
| 2 | 18 | 27 | 48 |
| 3 | 9 | 27 | 24 |
| 3 | 9 | 8 |
| 2 | 36 | 54 | 96 |
| 2 | 18 | 27 | 48 |
| 3 | 9 | 27 | 24 |
| 3 | 3 | 9 | 8 |
| 1 | 3 | 8 |
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 = 36 · 54 · 96 = 864
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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