Question

The GCD and LCM of two numbers a & b are respectively, 27 and 2079. If a is divided by 9 then the quotient is 21. Then b is:
(a) 243
(b) 189
(c) 113
(d) 297

Answer 1

Hint: We know that multiplication of GCD & LCM of two numbers gives the product of the two numbers so multiplying 27 with 2079 will give the product of a & b. Now, we can find the value of “a” by the formula $dividend=divisor\times quotient+remainder$ so $a=9\times 21+0$. We have the value of “a” and the product of “a” and “b” so we can find the value of “b”.

Complete step-by-step answer:
The GCD of two numbers (a & b) is given as 27.
The LCM of two numbers (a & b) is given as 2079.
We know that the product of GCD and LCM gives the product of two numbers i.e. $a\times b$.
$27\times 2079=a\times b$………… Eq. (1)
It is given that dividing “a” by 9 gives the quotient 21 so with this information we can find the value of “a” by the given formula.
$dividend=divisor\times quotient+remainder$
With the above information, the dividend is equal to “a”, the divisor is equal to 9, the quotient is equal to 21 and the remainder is equal to 0. Substituting these values in the above equation we get,
$a=9\times 21+0$
$\Rightarrow a=9\times 21$
Now, substituting the value of “a” in the eq. (1) we get,
$27\times 2079=9\times 21\times b$
$\begin{align}
  & \Rightarrow \dfrac{27\times 2079}{9\times 21}=b \\
 & \Rightarrow b=297 \\
\end{align}$
From the above solution, the value of “b” that we are getting is 297.
Hence, the correct option is (d).

Note: In this problem, we have interpreted the language of question “a is divided by 9 then the quotient is 21” as when “a” is divided by 9 then the quotient is 21 and remainder is 0. The question has not explicitly mentioned that the remainder is 0 but we have interpreted that the remainder is 0 and we are landing with a correct option so our interpretation is correct so sometimes in the problem, we take some things according to the requirement of options as we did here.