Question
Find Least Common Multiple of 120 and 150 using ladder method..
Answer
LCM( 120, 150 ) = 600
Explanation
Step 1 : Place the numbers inside division bar:
| 120 | 150 |
Step 2 : Find a prime number which divides both numbers.
In this example we can divide by 2. If any number is not divisible by 2 write it down unchanged.
| 2 | 120 | 150 |
| 60 | 75 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 120 | 150 |
| 3 | 60 | 75 |
| 20 | 25 |
| 2 | 120 | 150 |
| 3 | 60 | 75 |
| 5 | 20 | 25 |
| 4 | 5 |
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 = 120 · 150 = 600
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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