Question

Find the smallest number
which when divides 28 and
22, leaving remainders 8
12 respectively.
​

Answer 1

Let smallest number is x. Acordingly:-.

x = a×28+8……………(1)

x= b× 32 +12……………(2)

from eq.(1)& (2)

28a+8 = 32b +12

28a-32b= 4

7a-8 b = 1

7a =8b +1

a= (8b+1)/7………………..(3)

If b=1 then a is not whole number.

b=2 “ “ “ “ “ “ “ “ “ “ “ “ ‘ “ “

× × × × × × × × × × × × × × × × ×

b=6 then a =7 . which is also whole number.

On putting a=7 in eq.(1) or b= 6 in eq. (2)

x=28×7 + 8

x= 196 + 8

x = 204 , Answer.

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Answer 2

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