Question

Highest common factor and lowest common multiple of two numbers are 18 and 1782 respectively. One number is 162, find the other.

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Second Number is 198.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Highest Common Factor of the Numbers = 18

Lowest Common Factor of the Numbers = 1782

One Number = 162

To Find :

The Second Number

Solution :

Consider the Second Number as x

★ $\boxed{\sf{HCF \times LCM = Product\:of\:2\:numbers}}$

$\tt{\longrightarrow} \: 18 \times 1782 = 162 \times x$

$\tt{\longrightarrow} \:32076 = 162x$

$\tt{\longrightarrow} \: x = \dfrac{32076}{162}$

$\tt{\longrightarrow} \:x = 198$

$\therefore$ The Second Number is 198.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Place the value of x

$\tt{\longrightarrow} \:18 \times 1782 = 162 \times 198$

$\tt{\longrightarrow} \: 32076 = 32076$

$\therefore$ The Second Number is 198.