Find Least Common Multiple of 54, 306, 42, 196, 45, 600, 32 and 722 using division method..
Answer
LCM( 54, 306, 42, 196, 45, 600, 32, 722 ) = 6495400800
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 54 | 306 | 42 | 196 | 45 | 600 | 32 | 722 |
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 | 54 | 306 | 42 | 196 | 45 | 600 | 32 | 722 |
| 27 | 153 | 21 | 98 | 45 | 300 | 16 | 361 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 54 | 306 | 42 | 196 | 45 | 600 | 32 | 722 |
| 2 | 27 | 153 | 21 | 98 | 45 | 300 | 16 | 361 |
| 2 | 27 | 153 | 21 | 49 | 45 | 150 | 8 | 361 |
| 2 | 27 | 153 | 21 | 49 | 45 | 75 | 4 | 361 |
| 2 | 27 | 153 | 21 | 49 | 45 | 75 | 2 | 361 |
| 3 | 27 | 153 | 21 | 49 | 45 | 75 | 1 | 361 |
| 3 | 9 | 51 | 7 | 49 | 15 | 25 | 1 | 361 |
| 3 | 3 | 17 | 7 | 49 | 5 | 25 | 1 | 361 |
| 5 | 1 | 17 | 7 | 49 | 5 | 25 | 1 | 361 |
| 5 | 1 | 17 | 7 | 49 | 1 | 5 | 1 | 361 |
| 7 | 1 | 17 | 7 | 49 | 1 | 1 | 1 | 361 |
| 7 | 1 | 17 | 1 | 7 | 1 | 1 | 1 | 361 |
| 17 | 1 | 17 | 1 | 1 | 1 | 1 | 1 | 361 |
| 19 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 361 |
| 19 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 19 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 54, 306, 42, 196, 45, 600, 32, 722 ) = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 5 · 7 · 7 · 17 · 19 · 19 = 6495400800 .
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