Question
Find Least Common Multiple of 76, 144, 95 and 190 using prime factorisation method.
Answer
LCM( 76, 144, 95, 190 ) = 13680
Explanation
Step 1: Write down factorisation of each number:
76 = 2 · 2 · 19
144 = 2 · 2 · 2 · 2 · 3 · 3
95 = 5 · 19
190 = 2 · 5 · 19
Step 2 : Match primes vertically:
| 76 | = | 2 | · | 2 | · | 19 | ||||||||||
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
| 95 | = | 5 | · | 19 | ||||||||||||
| 190 | = | 2 | · | 5 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 76 | = | 2 | · | 2 | · | 19 | ||||||||||||
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 95 | = | 5 | · | 19 | ||||||||||||||
| 190 | = | 2 | · | 5 | · | 19 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 19 | = | 13680 |
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