Find Least Common Multiple of 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 using ladder method..
Answer
LCM( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ) = 2520
Explanation
Step 1 : Place the numbers inside division bar:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
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 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 1 | 3 | 2 | 5 | 3 | 7 | 4 | 9 | 5 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 1 | 1 | 3 | 2 | 5 | 3 | 7 | 4 | 9 | 5 |
| 1 | 1 | 3 | 1 | 5 | 3 | 7 | 2 | 9 | 5 |
| 2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 1 | 1 | 3 | 2 | 5 | 3 | 7 | 4 | 9 | 5 |
| 3 | 1 | 1 | 3 | 1 | 5 | 3 | 7 | 2 | 9 | 5 |
| 1 | 1 | 1 | 1 | 5 | 1 | 7 | 2 | 3 | 5 |
| 2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 1 | 1 | 3 | 2 | 5 | 3 | 7 | 4 | 9 | 5 |
| 3 | 1 | 1 | 3 | 1 | 5 | 3 | 7 | 2 | 9 | 5 |
| 5 | 1 | 1 | 1 | 1 | 5 | 1 | 7 | 2 | 3 | 5 |
| 1 | 1 | 1 | 1 | 1 | 1 | 7 | 2 | 3 | 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 = 1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 = 2520
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