Question
Find Least Common Multiple of 16, 20 and 80 using ladder method..
Answer
LCM( 16, 20, 80 ) = 80
Explanation
Step 1 : Place the numbers inside division bar:
| 16 | 20 | 80 |
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 | 16 | 20 | 80 |
| 8 | 10 | 40 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 16 | 20 | 80 |
| 2 | 8 | 10 | 40 |
| 4 | 5 | 20 |
| 2 | 16 | 20 | 80 |
| 2 | 8 | 10 | 40 |
| 2 | 4 | 5 | 20 |
| 2 | 5 | 10 |
| 2 | 16 | 20 | 80 |
| 2 | 8 | 10 | 40 |
| 2 | 4 | 5 | 20 |
| 2 | 2 | 5 | 10 |
| 1 | 5 | 5 |
| 2 | 16 | 20 | 80 |
| 2 | 8 | 10 | 40 |
| 2 | 4 | 5 | 20 |
| 2 | 2 | 5 | 10 |
| 5 | 1 | 5 | 5 |
| 1 | 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 = 16 · 20 · 80 = 80
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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