Question
Find Least Common Multiple of 12, 15, 90, 108, 135 and 150 using prime factorisation method.
Answer
LCM( 12, 15, 90, 108, 135, 150 ) = 2700
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
15 = 3 · 5
90 = 2 · 3 · 3 · 5
108 = 2 · 2 · 3 · 3 · 3
135 = 3 · 3 · 3 · 5
150 = 2 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 15 | = | 3 | · | 5 | ||||||||||
| 90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||
| 135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||
| 150 | = | 2 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||
| 15 | = | 3 | · | 5 | ||||||||||||
| 90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||||
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||||
| 150 | = | 2 | · | 3 | · | 5 | · | 5 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | = | 2700 |
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