Find Least Common Multiple of 48, 60 and 75 using division method..
Answer
LCM( 48, 60, 75 ) = 1200
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 48 | 60 | 75 |
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 | 48 | 60 | 75 |
| 24 | 30 | 75 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 48 | 60 | 75 |
| 2 | 24 | 30 | 75 |
| 2 | 12 | 15 | 75 |
| 2 | 6 | 15 | 75 |
| 3 | 3 | 15 | 75 |
| 5 | 1 | 5 | 25 |
| 5 | 1 | 1 | 5 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 48, 60, 75 ) = 2 · 2 · 2 · 2 · 3 · 5 · 5 = 1200 .
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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