Question
Find Least Common Multiple of 160, 320 and 410 using division method..
Answer
LCM( 160, 320, 410 ) = 13120
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 160 | 320 | 410 |
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 | 160 | 320 | 410 |
| 80 | 160 | 205 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 160 | 320 | 410 |
| 2 | 80 | 160 | 205 |
| 2 | 40 | 80 | 205 |
| 2 | 20 | 40 | 205 |
| 2 | 10 | 20 | 205 |
| 2 | 5 | 10 | 205 |
| 5 | 5 | 5 | 205 |
| 41 | 1 | 1 | 41 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 160, 320, 410 ) = 2 · 2 · 2 · 2 · 2 · 2 · 5 · 41 = 13120 .
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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