Question
Find Least Common Multiple of 290, 480 and 360 using ladder method..
Answer
LCM( 290, 480, 360 ) = 41760
Explanation
Step 1 : Place the numbers inside division bar:
| 290 | 480 | 360 |
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 | 290 | 480 | 360 |
| 145 | 240 | 180 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 290 | 480 | 360 |
| 2 | 145 | 240 | 180 |
| 145 | 120 | 90 |
| 2 | 290 | 480 | 360 |
| 2 | 145 | 240 | 180 |
| 2 | 145 | 120 | 90 |
| 145 | 60 | 45 |
| 2 | 290 | 480 | 360 |
| 2 | 145 | 240 | 180 |
| 2 | 145 | 120 | 90 |
| 5 | 145 | 60 | 45 |
| 29 | 12 | 9 |
| 2 | 290 | 480 | 360 |
| 2 | 145 | 240 | 180 |
| 2 | 145 | 120 | 90 |
| 5 | 145 | 60 | 45 |
| 3 | 29 | 12 | 9 |
| 29 | 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 = 290 · 480 · 360 = 41760
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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