Question
Find Least Common Multiple of 21870 and 9720 using ladder method..
Answer
LCM( 21870, 9720 ) = 87480
Explanation
Step 1 : Place the numbers inside division bar:
| 21870 | 9720 |
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 | 21870 | 9720 |
| 10935 | 4860 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 21870 | 9720 |
| 3 | 10935 | 4860 |
| 3645 | 1620 |
| 2 | 21870 | 9720 |
| 3 | 10935 | 4860 |
| 3 | 3645 | 1620 |
| 1215 | 540 |
| 2 | 21870 | 9720 |
| 3 | 10935 | 4860 |
| 3 | 3645 | 1620 |
| 3 | 1215 | 540 |
| 405 | 180 |
| 2 | 21870 | 9720 |
| 3 | 10935 | 4860 |
| 3 | 3645 | 1620 |
| 3 | 1215 | 540 |
| 3 | 405 | 180 |
| 135 | 60 |
| 2 | 21870 | 9720 |
| 3 | 10935 | 4860 |
| 3 | 3645 | 1620 |
| 3 | 1215 | 540 |
| 3 | 405 | 180 |
| 3 | 135 | 60 |
| 45 | 20 |
| 2 | 21870 | 9720 |
| 3 | 10935 | 4860 |
| 3 | 3645 | 1620 |
| 3 | 1215 | 540 |
| 3 | 405 | 180 |
| 3 | 135 | 60 |
| 5 | 45 | 20 |
| 9 | 4 |
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 = 21870 · 9720 = 87480
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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