Question

Find the smallest number which when divided by $42$ and $54$ leaves the remainders $34$ and $46$ respectively.

Answer 1

First, we need to fond the LCM of $42$ and $54$. The LCM of $42$ and $54$ is $378$.
Now, we shall find the difference of $42$ and $34$ which is $8$. Similarly, the difference of $54$ and $46$ is also $8$.
The difference of the LCM and $8$ is the smallest number.
So, $378-8=370$.
Hence, $370$ is the smallest number when divided by $42$ and $54$ leave remainders $34$ and $46$ respectively.