Question
Find Least Common Multiple of 1763 and 464268420 using division method..
Answer
LCM( 1763, 464268420 ) = 464268420
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1763 | 464268420 |
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 | 1763 | 464268420 |
| 1763 | 232134210 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1763 | 464268420 |
| 2 | 1763 | 232134210 |
| 3 | 1763 | 116067105 |
| 3 | 1763 | 38689035 |
| 5 | 1763 | 12896345 |
| 7 | 1763 | 2579269 |
| 11 | 1763 | 368467 |
| 19 | 1763 | 33497 |
| 41 | 1763 | 1763 |
| 43 | 43 | 43 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1763, 464268420 ) = 2 · 2 · 3 · 3 · 5 · 7 · 11 · 19 · 41 · 43 = 464268420 .
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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