Question
Find Least Common Multiple of 5, 10, 30 and 40 using prime factorisation method.
Answer
LCM( 5, 10, 30, 40 ) = 120
Explanation
Step 1: Write down factorisation of each number:
5 = 5
10 = 2 · 5
30 = 2 · 3 · 5
40 = 2 · 2 · 2 · 5
Step 2 : Match primes vertically:
| 5 | = | 5 | ||||||||
| 10 | = | 2 | · | 5 | ||||||
| 30 | = | 2 | · | 3 | · | 5 | ||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 5 | = | 5 | ||||||||||
| 10 | = | 2 | · | 5 | ||||||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | = | 120 |
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