Question

What is the number x
1. The LCM of x and 18 is 36.
2. The HCF of x and 18 is 2.
a) 1
b) 2
c) 3
d) 4

Answer 1

Hint: Here we have to determine the value of x such that we have the value of the LCM and HCF of the two numbers and we know the one term and another term is x. By using the formula
\[lcm(a,b) = \dfrac{{|a.b|}}{{\gcd (a,b)}}\] and by substituting the known values we obtain the solution for the given question and hence we choose the correct option.

Complete step-by-step solution:
The LCM is the least common multiple and HCF is the highest common factor.
Now consider the given question.
The LCM of x and 18 is 36. Generally it is written as \[lcm(x,18) = 36\]
The HCF of x and 18 is 2. Generally it is written as \[\gcd (x,18) = 2\]. The HCF is also called GCD which means the greatest common difference.
As we know that the formula for the LCM and it is given by \[lcm(a,b) = \dfrac{{|a.b|}}{{\gcd (a,b)}}\]
Here the value of a is x and the value of b is 18. On considering the formula we have
\[ \Rightarrow lcm(x,18) = \dfrac{{|x.18|}}{{\gcd (x,18)}}\]
On simplifying we have
\[ \Rightarrow 36 = \dfrac{{18x}}{2}\]
\[ \Rightarrow 36 = 9x\]
On dividing the above term by 9
\[ \Rightarrow x = 4\]
Therefore the value of x is 4.
Hence the option d) is the correct one.

Note: We can verify the obtained answer. The numbers are 4 and 18. We will find the LCM of two numbers. By using the formula \[lcm(a,b) = \dfrac{{|a.b|}}{{\gcd (a,b)}}\]. On substituting the values of a and b. We have \[lcm(4,18) = \dfrac{{|4.18|}}{2}\]On simplifying we get \[lcm(4,18) = \dfrac{{72}}{2} = 36\]. Hence verified.