Question

The HCF and LCM of two numbers is 18 and 1782 respectively. If one
number is 162, find the other number

Answer 1

Answer:

The Second Number is 198.

Step-by-step explanation:

Given :

• Highest Common Factor of the Numbers = 18
• Lowest Common Multiple of the Numbers = 1782
• One Number = 162

To Find :

• The Second Number

Solution :

Consider the Second Number as x

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

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

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

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

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

∴ The Second Number is 198.

____________________________

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

Place the value of x

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

$\tt{\longrightarrow\:HCF \times LCM = Product\:of\:2\:numbers}$

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

∴ The Second Number is 198.

Answer 2

$\sf\small\underline{given \::-} \:$

• HCF = 18
• lcm = 1782
• one number = 162

$\sf\small\underline{to \: find : - \: }$

• other number

$\sf\small\underline{formula : - \: }$

$\sf \: hcf \: \times lcm \: = product \: of \: two \: number \:$

$\sf\small\underline{solution:- \: }$

let the other number be X

now by using formula :-

$\sf \: hcf \: \times lcm \: = product \: of \: two \: number \:$

$\: \: \: \: \: \: \: \: :\implies\sf \: 18 \times 1782 = 16 \times x \\ \\ \\ \: \: \: \: \: \: \: \: :\implies\sf x = 18 \times \frac{1782}{162} \\ \\ \\ \: \: \: \: \: \: \: \: :\implies\sf \: x = \cancel \frac{32076}{162} \\ \\ \\ \: \: \: \: \: \: \: \: :\implies\sf \: x = 198$

$\sf\small\underline{verification : - \: }$

$\: \: \: \: \: \: \: \: \: \: :\implies\sf \:hcf \: \times lcm = product \: of \: two \: number \: \\ \\ \\ \: \: \: \: \: \: \: \: \: \: :\implies\sf \: \: 18 \times 1782 = 162 \times 198 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: :\implies\sf \: \: 32076 = 32076$

∴ second number is 198