Question

Find the least positive integer that is divisible by both $2$ and $5$ and leaves a remainder of $2$ when it is divided by $7$.

• A. $20$
• B. $30$
• C. $50$
• D. $65$
• E. $75$

Answer 1

Answer: (B)

$30$

Let the least positive number be $n$, given that when $n$ is divided with $7$, the remainder is $2$. So we get $n=7k+2$ (where $k$ is integer).

Now we should select least positive value of $k$ such that $n$ must be divisible by $2$ and $5$.
We can observe that $k=5$ is the least value of $k$ for which $n$ will be divisible by both $2$ and $5$.
Therefore for $k=5$, we get $n=30$