HCF of three numbers is 3 and LCM is 27. Find the product of the three numbers.
Question
HCF of three numbers is 3 and LCM is 27.
Find the product of the three numbers.
Solution
1. Break Down the Problem
We need to find the product of three numbers given their Highest Common Factor (HCF) and Least Common Multiple (LCM). The HCF of the three numbers is 3 and the LCM is 27.
2. Relevant Concepts
The relationship between the product of the numbers, their HCF, and their LCM is given by the formula:
where is the number of numbers. For three numbers, .
3. Analysis and Detail
Substituting the known values into the formula:
- HCF = 3
- LCM = 27
Thus, the product of the three numbers can be calculated as:
Calculating :
Now, substituting back to find the product:
Calculating :
4. Verify and Summarize
Thus, the calculations confirm that the product of the three numbers is 59049, and it consists of the HCF and the LCM correctly applied.
Final Answer
The product of the three numbers is 59049.
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