Question
Find Least Common Multiple of 42, 56 and 84 using ladder method..
Answer
LCM( 42, 56, 84 ) = 168
Explanation
Step 1 : Place the numbers inside division bar:
| 42 | 56 | 84 |
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 | 42 | 56 | 84 |
| 21 | 28 | 42 |
Step 3 : Repeat Step 2 until you can no longer divide.
| 2 | 42 | 56 | 84 |
| 2 | 21 | 28 | 42 |
| 21 | 14 | 21 |
| 2 | 42 | 56 | 84 |
| 2 | 21 | 28 | 42 |
| 3 | 21 | 14 | 21 |
| 7 | 14 | 7 |
| 2 | 42 | 56 | 84 |
| 2 | 21 | 28 | 42 |
| 3 | 21 | 14 | 21 |
| 7 | 7 | 14 | 7 |
| 1 | 2 | 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 = 42 · 56 · 84 = 168
This solution can be visualized using a Venn diagram.
0,0
42
56
84
2
7
3
2
2
The LCM is equal to the product of all the numbers on the diagram.
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