Question
Find Least Common Multiple of 1, 75, 1, 265, 1 and 115 using prime factorisation method.
Answer
LCM( 1, 75, 1, 265, 1, 115 ) = 91425
Explanation
Step 1: Write down factorisation of each number:
1 = 1
75 = 3 · 5 · 5
1 = 1
265 = 5 · 53
1 = 1
115 = 5 · 23
Step 2 : Match primes vertically:
| 1 | = | 1 | ||||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||
| 265 | = | 5 | · | 53 | ||||||||
| 115 | = | 5 | · | 23 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 1 | = | 1 | ||||||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||
| 265 | = | 5 | · | 53 | ||||||||||
| 115 | = | 5 | · | 23 | ||||||||||
| LCM | = | 1 | · | 3 | · | 5 | · | 5 | · | 23 | · | 53 | = | 91425 |
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