Find Least Common Multiple of 12, 32 and 64 using prime factorisation method.
Answer
LCM( 12, 32, 64 ) = 192
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
32 = 2 · 2 · 2 · 2 · 2
64 = 2 · 2 · 2 · 2 · 2 · 2
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | = | 192 |
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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