Question

Find the lowest 4-digit number which when divided by $3,4$ or $5$ leaves a remainder of 2 in each case.

Answer 1

Lowest $4-$digit number is $1000$. LCM of $3,4$ and $5$ is $60.$

Dividing $1000$ by $60$ we get the remainder $40.$

Thus the lowest 4-digit number that exactly divisible by $3,4$ and $5$ is $1000+(60-40)=1020$.

Now add the remainder $2$ that's required. Thus the answer is $1022.$