Question

Find the value of x and state which of the given statement is/are required for it.
I. The L.C.M of x and 18 is 36.
II. The H.C.F of x and 18 is 2.

• A. 1, only statement-I is required
• B. 2 only statement-II is required
• C. 4, statement I and II both are required
• D. None of these

Answer 1

The correct option is C 4, statement I and II both are required

If a and b are two numbers then,
Product of a and b = L.C.M. of a and b $\times$ H.C.F. of a and b
$\therefore$ to find the unknown number, we need to know the second number, L.C.M. and H.C.F. of both the numbers.
So, we require both the statements to find the value of x.
Now, the L.C.M of x and 18 is 36 and the H.C.F of x and 18 is 2.
$\Rightarrow$ x $\times$ 18 = 36 $\times$ 2
$\Rightarrow$ x $\times$ 18 = 72
$\Rightarrow$ x = $\frac{72}{18}$
$\Rightarrow$ x = 4
$\therefore$ the value of x is 4.