Question
Find Least Common Multiple of 10, 15, 36, 81 and 121 using prime factorisation method.
Answer
LCM( 10, 15, 36, 81, 121 ) = 196020
Explanation
Step 1: Write down factorisation of each number:
10 = 2 · 5
15 = 3 · 5
36 = 2 · 2 · 3 · 3
81 = 3 · 3 · 3 · 3
121 = 11 · 11
Step 2 : Match primes vertically:
| 10 | = | 2 | · | 5 | ||||||||||||||
| 15 | = | 3 | · | 5 | ||||||||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||||||||
| 121 | = | 11 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 10 | = | 2 | · | 5 | ||||||||||||||||
| 15 | = | 3 | · | 5 | ||||||||||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||||||||||
| 121 | = | 11 | · | 11 | ||||||||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 11 | · | 11 | = | 196020 |
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