Question
Find Least Common Multiple of 25 and 75 using ladder method..
Answer
LCM( 25, 75 ) = 75
Explanation
Step 1 : Place the numbers inside division bar:
| 25 | 75 |
Step 2 : Find a prime number which divides both numbers.
In this example we can divide by 5. If any number is not divisible by 5 write it down unchanged.
| 5 | 25 | 75 |
| 5 | 15 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 5 | 25 | 75 |
| 5 | 5 | 15 |
| 1 | 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 = 25 · 75 = 75
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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