What is the smallest number (bigger than 1) that will leave a remainder of 1 when divided by any of 2, 3, 4, 5, or 6?

Question

My house number is such that, when divided by 2, 3, 4, 5 or 6 it will always leave a remainder of 1.

However, when divided by 11 there is no remainder.
What is my house number?

Answer 1

The smallest number which gives the remainder of 1 when divided of any of the numbers is the LCM of the numbers + 1
i.e. LCM + 1

Which is 61

why????

Because LCM is the smallest number divisible by all the given numbers...........and to have the remainder of 1 then add 1 to the LCM

2 = 1*2
3 = 1*3
4 = 1*2*2
5 = 1*5
6 = 1*2*3
so
LCM = 1*2*2*3*5 = 60
LCM + 1 = 61

So the number is 61

Answer 2

61 is the smallest number
The smallest number which gives the remainder of 1 when divided of any of the numbers is the LCM of the numbers + 1
i.e. LCM + 1
Which is 61