Find Least Common Multiple of 36, 48, 84 and 140 using prime factorisation method.
Answer
LCM( 36, 48, 84, 140 ) = 5040
Explanation
Step 1: Write down factorisation of each number:
36 = 2 · 2 · 3 · 3
48 = 2 · 2 · 2 · 2 · 3
84 = 2 · 2 · 3 · 7
140 = 2 · 2 · 5 · 7
Step 2 : Match primes vertically:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||
| 140 | = | 2 | · | 2 | · | 5 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||||
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||||
| 140 | = | 2 | · | 2 | · | 5 | · | 7 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 7 | = | 5040 |
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