Question

what is the lowest number, which when divided by 16 leaves remainder 2 and when divided by 18 leaves remainder 12 ?​

Answer 1

We want the smallest number, which, when divided by 1616 leaves a remainder of 22 and, which, when divided by 1818 leaves a remainder of 12.12.
Let that number be n.n.
⇒n=16s+2
⇒n=16s+2 for some ss∈N,∈N, 
and,
n=18t+12n=18t+12 for some t∈N.t∈N.
⇒16s+2=18t+12.
⇒16s+2=18t+12.
⇒16s−18t=10
⇒8s−9t=5.
⇒16s−18t=10
⇒8s−9t=5.
It can be seen that the least value of ss which satisfies this equation is 44 for which the corresponding value of tt is 3,3,
 since 8×4−9×3=32−27=5.8×4−9×3=32−27=5.
⇒n=16s+2=16×4+2=64+2=66.
⇒n=16s+2=16×4+2=64+2=66.
⇒⇒ The required number is 66.
Ram ram brothers