Question
Find Least Common Multiple of 56, 84 and 133 using division method..
Answer
LCM( 56, 84, 133 ) = 3192
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 56 | 84 | 133 |
Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 2.
(if any number is not divisible by 2, write it down unchanged)
| 2 | 56 | 84 | 133 |
| 28 | 42 | 133 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 56 | 84 | 133 |
| 2 | 28 | 42 | 133 |
| 2 | 14 | 21 | 133 |
| 3 | 7 | 21 | 133 |
| 7 | 7 | 7 | 133 |
| 19 | 1 | 1 | 19 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 56, 84, 133 ) = 2 · 2 · 2 · 3 · 7 · 19 = 3192 .
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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