Question
Find Least Common Multiple of 40, 75, 39 and 136 using prime factorisation method.
Answer
LCM( 40, 75, 39, 136 ) = 132600
Explanation
Step 1: Write down factorisation of each number:
40 = 2 · 2 · 2 · 5
75 = 3 · 5 · 5
39 = 3 · 13
136 = 2 · 2 · 2 · 17
Step 2 : Match primes vertically:
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||
| 39 | = | 3 | · | 13 | ||||||||||||
| 136 | = | 2 | · | 2 | · | 2 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||||
| 39 | = | 3 | · | 13 | ||||||||||||||
| 136 | = | 2 | · | 2 | · | 2 | · | 17 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 13 | · | 17 | = | 132600 |
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