Find Least Common Multiple of 9, 15, 25, 40 and 75 using prime factorisation method.
Answer
LCM( 9, 15, 25, 40, 75 ) = 1800
Explanation
Step 1: Write down factorisation of each number:
9 = 3 · 3
15 = 3 · 5
25 = 5 · 5
40 = 2 · 2 · 2 · 5
75 = 3 · 5 · 5
Step 2 : Match primes vertically:
| 9 | = | 3 | · | 3 | ||||||||||
| 15 | = | 3 | · | 5 | ||||||||||
| 25 | = | 5 | · | 5 | ||||||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||
| 75 | = | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 9 | = | 3 | · | 3 | ||||||||||||
| 15 | = | 3 | · | 5 | ||||||||||||
| 25 | = | 5 | · | 5 | ||||||||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | = | 1800 |
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