Find Least Common Multiple of 12, 15 and 75 using ladder method..
Answer
LCM( 12, 15, 75 ) = 300
Explanation
Step 1 : Place the numbers inside division bar:
| 12 | 15 | 75 |
Step 2 : Find a prime number which can divide at least two of your numbers.
In this example we can divide by 3. If any number is not divisible by 3 write it down unchanged.
| 3 | 12 | 15 | 75 |
| 4 | 5 | 25 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 3 | 12 | 15 | 75 |
| 5 | 4 | 5 | 25 |
| 4 | 1 | 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 = 12 · 15 · 75 = 300
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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