Question
Find Least Common Multiple of 72, 49 and 53 using division method..
Answer
LCM( 72, 49, 53 ) = 186984
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 72 | 49 | 53 |
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 | 72 | 49 | 53 |
| 36 | 49 | 53 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 72 | 49 | 53 |
| 2 | 36 | 49 | 53 |
| 2 | 18 | 49 | 53 |
| 3 | 9 | 49 | 53 |
| 3 | 3 | 49 | 53 |
| 7 | 1 | 49 | 53 |
| 7 | 1 | 7 | 53 |
| 53 | 1 | 1 | 53 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 72, 49, 53 ) = 2 · 2 · 2 · 3 · 3 · 7 · 7 · 53 = 186984 .
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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