Question
Find Least Common Multiple of 35, 48, 42 and 100 using prime factorisation method.
Answer
LCM( 35, 48, 42, 100 ) = 8400
Explanation
Step 1: Write down factorisation of each number:
35 = 5 · 7
48 = 2 · 2 · 2 · 2 · 3
42 = 2 · 3 · 7
100 = 2 · 2 · 5 · 5
Step 2 : Match primes vertically:
| 35 | = | 5 | · | 7 | ||||||||||||
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 42 | = | 2 | · | 3 | · | 7 | ||||||||||
| 100 | = | 2 | · | 2 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 35 | = | 5 | · | 7 | ||||||||||||||
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 42 | = | 2 | · | 3 | · | 7 | ||||||||||||
| 100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 7 | = | 8400 |
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