Question

Solve the answer for question given below ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given two positive integers are 117 and 63.

Let we first find the HCF of 117 and 63 using Euclid Division Algorithm,

$\red{\rm :\longmapsto\:117 = 63 \times 1 + 54}$

$\blue{\rm :\longmapsto\:63 = 54 \times 1 + 9}$

$\green{\rm :\longmapsto\:54 = 9 \times 6 + 0}$

Hence,

↝  HCF ( 117, 63 ) = 9

Now,

We represent the HCF 9 as a Linear Combination of 117 and 63.

So,

$\rm :\longmapsto\:9 = 63 - 54$

$\rm :\longmapsto\:9 = 63 - (117 - 63)$

$\rm :\longmapsto\:9 = 63 - 117 + 63$

$\rm :\longmapsto\:9 = 63 \times 2 - 117 \times 1$

$\rm :\longmapsto\:9 = 117 \times ( - 1) + 63 \times (2)$

$\bf :\longmapsto\:HCF ( 117, 63 ) = 117 \times ( - 1) + 63 \times (2)$

Now, it is given that

$\bf :\longmapsto\:HCF ( 117, 63 ) = 63 m + 117 n$

So, on comparing we get

$\red{\rm :\longmapsto\:m \: = \: 2}$

and

$\red{\rm :\longmapsto\:n \: = \: - \: 1}$

Thus,

$\red{\bf :\longmapsto\:m + n \: = \:2 \: - \: 1 \: = \:1 }$

Hence, Option (b) is correct

Additional Information :-

↝ 1. HCF ( a, b ) × LCM ( a, b ) = a × b

↝ 2. HCF always divides a, b and LCM

Answer 2

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