Question
Find Least Common Multiple of 35, 40, 90 and 120 using prime factorisation method.
Answer
LCM( 35, 40, 90, 120 ) = 2520
Explanation
Step 1: Write down factorisation of each number:
35 = 5 · 7
40 = 2 · 2 · 2 · 5
90 = 2 · 3 · 3 · 5
120 = 2 · 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
| 35 | = | 5 | · | 7 | ||||||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||
| 90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 35 | = | 5 | · | 7 | ||||||||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||
| 90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 7 | = | 2520 |
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