Find Least Common Multiple of 30, 1000, 100 and 86 using prime factorisation method.
Answer
LCM( 30, 1000, 100, 86 ) = 129000
Explanation
Step 1: Write down factorisation of each number:
30 = 2 · 3 · 5
1000 = 2 · 2 · 2 · 5 · 5 · 5
100 = 2 · 2 · 5 · 5
86 = 2 · 43
Step 2 : Match primes vertically:
| 30 | = | 2 | · | 3 | · | 5 | ||||||||||
| 1000 | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | · | 5 | ||||
| 100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||||
| 86 | = | 2 | · | 43 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 30 | = | 2 | · | 3 | · | 5 | ||||||||||||
| 1000 | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | · | 5 | ||||||
| 100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||||||
| 86 | = | 2 | · | 43 | ||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 5 | · | 43 | = | 129000 |
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