Find Least Common Multiple of 23, 12 and 33 using prime factorisation method.
Answer
LCM( 23, 12, 33 ) = 3036
Explanation
Step 1: Write down factorisation of each number:
23 = 23
12 = 2 · 2 · 3
33 = 3 · 11
Step 2 : Match primes vertically:
| 23 | = | 23 | ||||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||
| 33 | = | 3 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 23 | = | 23 | ||||||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| 33 | = | 3 | · | 11 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 11 | · | 23 | = | 3036 |
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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