Question

If $\left( {24,92} \right) = 24m + 92n$ , then find $\left( {m,n} \right)$ is
A.$\left( { - 1,4} \right)$
B.$\left( {4, - 1} \right)$
C.$\left( {4, - 3} \right)$
D.$\left( { - 4,3} \right)$

Answer 1

Hint: Here we have to first find the HCF of 24 and 92 as $\left({24,92}\right)$ denotes HCF of 24 and 92. Then find multiple of 24 nearest to 92 and then find the value of m and n

Complete step-by-step answer:
$\left( {24,92} \right)$ denotes the HCF of 24 and 92
$24 = {2^3} \times 3$
$92 = {2^2} \times 23$
HCF of 24 and 92 is 4
Now, the multiple of 24 nearest to 92 is 96
Substitute m and n as $\left( {24,92} \right) = 24m + 92n$
So we can say $24 \times 4 - 92 \times 1 = 4$
Hence $m = 4,n = - 1$
Therefore $\left( {m,n} \right) = \left( {4, - 1} \right)$
So the correct option is (B)
NOTE: To solve such problem we first have to find the HCF of two numbers then find the multiple which is nearest and divisible to one of the number and then substitute for m and n and find the value