Question

Given that HCF (253, 440) = 11 and LCM (253, 440) =$253\times R$. The value of R is:
a) 400
b) 40
c) 440
d) 253

Answer 1

Hint: The HCF of 2 numbers is the highest common factor and LCM is the least common multiple and LCM of the two numbers can be understood as HCF multiplies with the remaining uncommon factors of 2 numbers.

Complete step-by-step answer:
It is given that HCF (253, 440) = 11 and LCM (253, 440) =$253\times R$.
Now, the prime factorization of $253=11\times 23$
Prime factorization of:
$440=11\times 2\times 2\times 2\times 5$
LCM can be understood as HCF multiplied by uncommon factors so HCF (253, 440) is 11 and the uncommon factors are $23\times 2\times 2\times 2\times 5$. So, the LCM can be written as $11\times 23\times 2\times 2\times 2\times 5$ which is equal to 10120. But the LCM given in the question is in the form of $253\times R$ so we have to write the LCM in the form of $253\times R$ so if we carefully look the LCM expression $\underline{11\times 23}\times 2\times 2\times 2\times 5$then$11\times 23$ is equal to 253 and on comparing this LCM with $253\times R$ then R is the remaining multiplication which is shown by the not underlined expression in $\underline{11\times 23}\times 2\times 2\times 2\times 5$.
So, the value of R is $2\times 2\times 2\times 5$ which is equal to 40.
Hence, the value of R in the equation LCM (253, 440) =$253\times R$ is equal to 40.
Hence, the correct option is (b).

Note: There is an alternate way of solving the above question is:
 The product of the HCF and LCM of the two numbers is equivalent to the product of the two numbers.
So, HCF (253, 440)$\times $LCM (253, 440) = 253$\times $440
Substituting the values given in the question to above equation we get,
$\begin{align}
  & 11\times 253\times R=253\times 440 \\
 & \Rightarrow R=40 \\
\end{align}$