Find Least Common Multiple of 24, 45 and 72 using ladder method..
Answer
LCM( 24, 45, 72 ) = 360
Explanation
Step 1 : Place the numbers inside division bar:
| 24 | 45 | 72 |
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 | 24 | 45 | 72 |
| 12 | 45 | 36 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 24 | 45 | 72 |
| 2 | 12 | 45 | 36 |
| 6 | 45 | 18 |
| 2 | 24 | 45 | 72 |
| 2 | 12 | 45 | 36 |
| 2 | 6 | 45 | 18 |
| 3 | 45 | 9 |
| 2 | 24 | 45 | 72 |
| 2 | 12 | 45 | 36 |
| 2 | 6 | 45 | 18 |
| 3 | 3 | 45 | 9 |
| 1 | 15 | 3 |
| 2 | 24 | 45 | 72 |
| 2 | 12 | 45 | 36 |
| 2 | 6 | 45 | 18 |
| 3 | 3 | 45 | 9 |
| 3 | 1 | 15 | 3 |
| 1 | 5 | 1 |
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 = 24 · 45 · 72 = 360
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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