Question
Find Least Common Multiple of 1, 40, 1, 30, 1, 50, 1 and 40 using prime factorisation method.
Answer
LCM( 1, 40, 1, 30, 1, 50, 1, 40 ) = 600
Explanation
Step 1: Write down factorisation of each number:
1 = 1
40 = 2 · 2 · 2 · 5
1 = 1
30 = 2 · 3 · 5
1 = 1
50 = 2 · 5 · 5
1 = 1
40 = 2 · 2 · 2 · 5
Step 2 : Match primes vertically:
| 1 | = | 1 | ||||||||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||||
| 50 | = | 2 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 1 | = | 1 | ||||||||||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||||||
| 50 | = | 2 | · | 5 | · | 5 | ||||||||||
| LCM | = | 1 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | = | 600 |
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