Question

find the smallest 5 digit number which when divided by 16 32 18 24 and 36 leaves remainder 6 in each case answer will 10036 but how explain it​

Answer 1

MARK ME AS A BRAINLIEST

Step-by-step explanation:

Let the Smallest number be X.

Expressing the equation in the language of Modular Airthmatic, we can write

X=5 (mod 16)

X=5 (mod 18)

X=5 (mod 32)

Since the REMAINDER is same, the above congruences can be combined into one congruence as,

X=5 ( LCM of 16,18,32)

X=5 (mod 288)

The above equality can be written in Parametric Form as,

X=5+288 t where t is any integer.

For X to be SMALLEST, take

t=0

X= 5.

Therefore the SMALLEST number is 5□Ans.

[In fact, if negative numbers are permitted, there are INFINITY Solutions on the Number Line ]