Find Least Common Multiple of 40, 48 and 45 using ladder method..
Answer
LCM( 40, 48, 45 ) = 720
Explanation
Step 1 : Place the numbers inside division bar:
| 40 | 48 | 45 |
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 | 40 | 48 | 45 |
| 20 | 24 | 45 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 40 | 48 | 45 |
| 2 | 20 | 24 | 45 |
| 10 | 12 | 45 |
| 2 | 40 | 48 | 45 |
| 2 | 20 | 24 | 45 |
| 2 | 10 | 12 | 45 |
| 5 | 6 | 45 |
| 2 | 40 | 48 | 45 |
| 2 | 20 | 24 | 45 |
| 2 | 10 | 12 | 45 |
| 5 | 5 | 6 | 45 |
| 1 | 6 | 9 |
| 2 | 40 | 48 | 45 |
| 2 | 20 | 24 | 45 |
| 2 | 10 | 12 | 45 |
| 5 | 5 | 6 | 45 |
| 3 | 1 | 6 | 9 |
| 1 | 2 | 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 = 40 · 48 · 45 = 720
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
This page was created using
LCM Calculator