Find Least Common Multiple of 32, 34 and 36 using prime factorisation method.
Answer
LCM( 32, 34, 36 ) = 4896
Explanation
Step 1: Write down factorisation of each number:
32 = 2 · 2 · 2 · 2 · 2
34 = 2 · 17
36 = 2 · 2 · 3 · 3
Step 2 : Match primes vertically:
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 34 | = | 2 | · | 17 | ||||||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 34 | = | 2 | · | 17 | ||||||||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 17 | = | 4896 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
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