Question

The least number which when divided by $2,3,4,5$ and $6$ leaves the remainder $1$ in each case. If the same number is divided by $7,$ it leaves no remainder. The number is

• A. $231$
• B. $301$
• C. $371$
• D. $441$

Answer 1

Answer: (B)

$301$

For finding the least number which is divisible by $2,3,4,5,6$ we need to find the LCM of these numbers and we get $60$ is divisible by $2,3,4,5,6.$

Now according to question, it leaves the remainder $1.$

So, required number is $61$ but it has to divisible by $7.$

Let the general number be $60n+1$ which is divisible by $7$ and leaves remainder $1$ when divided by $2,3,4,5,6$

Now look at option and find out the least number which is of form $60n+1.$

$\therefore$ $B$ is correct.