Question

The LCM of two numbers is 2079 and their HCF is 27. If the first number is 189. Then, the second number is
A. 295
B. 296
C. 297
D. None of the above

Answer 1

Hint: LCM and HCF of two numbers are given i.e. 2079 and 27 respectively. Objective is to find the second number if the first number is 189. To solve this problem, we’ll use one formula that involves LCM, HCF & these two numbers. Using this formula, we can simply find out the second number & can find out the correct option mentioned in the above question.
The formula is Product of LCM and HCF of two numbers is equal to product of that two numbers.
\[\left( \text{LCM}\times \text{HCF} \right)=(\operatorname{Product}\text{ of two numbers)}\]
Complete step by step solution:
We can write the given data below as,
\[\begin{align}
  & LCM=2079 \\
 & HCF=27 \\
 & Second\text{ }number=\dfrac{\left( LCM\times HCF \right)}{First\text{ }Number} \\
\end{align}\]
Now, let us substitute the known values in the above equation to get the second number.
\[\begin{align}
  & Second\text{ }Number=\left( \dfrac{2079\times 27}{189} \right) \\
 & =\left( \dfrac{2079\times 3}{21} \right) \\
 & =\left( \dfrac{2079}{7} \right) \\
 & =297 \\
\end{align}\]

Hence, the second number is 297. If the first number, LCM and HCF are 189, 2079 & 27 respectively.

Therefore, Option C is the correct one.

Note: In the above question, we had to find out the second number. But in some questions, the first number, second number and HCF of the two numbers would be given, and the objective would be to find out the LCM of these two numbers. For this, we can have two methods.
1. We can simply find out the LCM of two numbers using basic methods, as both numbers are already given in the question itself.
2. We can willingly use the above-mentioned formula to find out LCM of those two numbers. For finding LCM, formula would be the product of two numbers divided by HCF of two numbers given in the question.