Question
Find Least Common Multiple of 15, 16 and 36 using ladder method..
Answer
LCM( 15, 16, 36 ) = 720
Explanation
Step 1 : Place the numbers inside division bar:
| 15 | 16 | 36 |
Step 2 : Find a prime number which can divide at least two of your numbers.
In this example we can divide by 3. If any number is not divisible by 3 write it down unchanged.
| 3 | 15 | 16 | 36 |
| 5 | 16 | 12 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 3 | 15 | 16 | 36 |
| 2 | 5 | 16 | 12 |
| 5 | 8 | 6 |
| 3 | 15 | 16 | 36 |
| 2 | 5 | 16 | 12 |
| 2 | 5 | 8 | 6 |
| 5 | 4 | 3 |
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 = 15 · 16 · 36 = 720
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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