Question

Hcf of two numbers is 13 and their lcm is 182. If one of the number is 26, then find the other number.

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

$\text{The second number is 91}$

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given :}}}$

HCF if the numbers = 13

LCM of the numbers = 182

One number = 26

$\textsf{\underline{\underline{To find :}}}$

The second number

$\textsf{\underline{\underline{Solution :}}}$

Consider the Second number as x

There is a relation between the LCM and HCF.

The product of two given numbers is equal to the product of their HCF and LCM.

$\star$Product of two numbers = LCM × HCF

$\tt{\implies26 \times x = 13 \times 182}$

$\tt{\implies26x = 2366}$

$\tt{\implies \: x = \dfrac{2322}{26} }$

$\tt{\implies \: x = 91}$

$\large{\boxed{\bigstar{\sf \: {x = 91}}}}$

$\therefore$$\text{The second number is 91}$

$\textbf{\underline{\underline{Verification :-}}}$

$\tt{\implies26 \times 91 = 13 \times 182}$

$\tt{\implies2366 = 2366}$

${\boxed{\bigstar{\sf \: {LHS = RHS }}}}$

$\therefore$$\text{The second number is 91}$

⟩⟩ Extra info ⟨⟨

• LCM stands for - Least Common Multiple.

• The LCM of two numbers is the smallest number that is a multiple of both the numbers.

• HCF stands for Highest Common Factors.

• It can be used to reduce fractions.

Answer 2

$\mathfrak{Answer:}$

= 91.

$\mathfrak{Step-by-Step\:Explanation:}$

$\underline{\bold{Given\;in\:the\:question:}}$

• H.C.F of two numbers = 13.
• Their L.C.M = 182
• First no. = 26.

$\bold{Solution:}$

Let the second no. be x .

$\mathfrak{According\:to\:question:}\\\\\\\boxed{\bold{H.C.F\:\times\:L.C.M=1st\;number\times2nd\:number.}}\\\\\\\implies\tt{13\times 182=26\times x}\\\\\\\implies\tt{x=\dfrac{13\times 182}{26}}\\\\\\\implies\tt{x=91.}\\\\\\\\\boxed{\boxed{\bold{Other\:no.=91.}}}$