Question
Find Least Common Multiple of 81, 125, 525 and 172 using prime factorisation method.
Answer
LCM( 81, 125, 525, 172 ) = 12190500
Explanation
Step 1: Write down factorisation of each number:
81 = 3 · 3 · 3 · 3
125 = 5 · 5 · 5
525 = 3 · 5 · 5 · 7
172 = 2 · 2 · 43
Step 2 : Match primes vertically:
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||||||||||||
| 125 | = | 5 | · | 5 | · | 5 | ||||||||||||||||
| 525 | = | 3 | · | 5 | · | 5 | · | 7 | ||||||||||||||
| 172 | = | 2 | · | 2 | · | 43 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||||||||||||||
| 125 | = | 5 | · | 5 | · | 5 | ||||||||||||||||||
| 525 | = | 3 | · | 5 | · | 5 | · | 7 | ||||||||||||||||
| 172 | = | 2 | · | 2 | · | 43 | ||||||||||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 7 | · | 43 | = | 12190500 |
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