Question
Find Least Common Multiple of 72, 85 and 90 using ladder method..
Answer
LCM( 72, 85, 90 ) = 6120
Explanation
Step 1 : Place the numbers inside division bar:
| 72 | 85 | 90 |
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 | 72 | 85 | 90 |
| 36 | 85 | 45 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 72 | 85 | 90 |
| 3 | 36 | 85 | 45 |
| 12 | 85 | 15 |
| 2 | 72 | 85 | 90 |
| 3 | 36 | 85 | 45 |
| 3 | 12 | 85 | 15 |
| 4 | 85 | 5 |
| 2 | 72 | 85 | 90 |
| 3 | 36 | 85 | 45 |
| 3 | 12 | 85 | 15 |
| 5 | 4 | 85 | 5 |
| 4 | 17 | 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 = 72 · 85 · 90 = 6120
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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