Find Least Common Multiple of 45, 117, 221, 357, 525 and 725 using prime factorisation method.
Answer
LCM( 45, 117, 221, 357, 525, 725 ) = 10094175
Explanation
Step 1: Write down factorisation of each number:
45 = 3 · 3 · 5
117 = 3 · 3 · 13
221 = 13 · 17
357 = 3 · 7 · 17
525 = 3 · 5 · 5 · 7
725 = 5 · 5 · 29
Step 2 : Match primes vertically:
| 45 | = | 3 | · | 3 | · | 5 | ||||||||||
| 117 | = | 3 | · | 3 | · | 13 | ||||||||||
| 221 | = | 13 | · | 17 | ||||||||||||
| 357 | = | 3 | · | 7 | · | 17 | ||||||||||
| 525 | = | 3 | · | 5 | · | 5 | · | 7 | ||||||||
| 725 | = | 5 | · | 5 | · | 29 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 45 | = | 3 | · | 3 | · | 5 | ||||||||||||
| 117 | = | 3 | · | 3 | · | 13 | ||||||||||||
| 221 | = | 13 | · | 17 | ||||||||||||||
| 357 | = | 3 | · | 7 | · | 17 | ||||||||||||
| 525 | = | 3 | · | 5 | · | 5 | · | 7 | ||||||||||
| 725 | = | 5 | · | 5 | · | 29 | ||||||||||||
| LCM | = | 3 | · | 3 | · | 5 | · | 5 | · | 7 | · | 13 | · | 17 | · | 29 | = | 10094175 |
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