Find Least Common Multiple of 2, 25, 4, 5, 2 and 75 using prime factorisation method.
Answer
LCM( 2, 25, 4, 5, 2, 75 ) = 300
Explanation
Step 1: Write down factorisation of each number:
2 = 2
25 = 5 · 5
4 = 2 · 2
5 = 5
2 = 2
75 = 3 · 5 · 5
Step 2 : Match primes vertically:
| 2 | = | 2 | ||||||||
| 25 | = | 5 | · | 5 | ||||||
| 4 | = | 2 | · | 2 | ||||||
| 5 | = | 5 | ||||||||
| 75 | = | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 2 | = | 2 | ||||||||||
| 25 | = | 5 | · | 5 | ||||||||
| 4 | = | 2 | · | 2 | ||||||||
| 5 | = | 5 | ||||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | = | 300 |
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