how many eggs did the farmer have

Question

she had no eggs left over with a group of seven but she had one egg left over with a group of 2,3,4,5, & 6 .

Answer 1

There is probably a better way to do this but:

since it leave a remainder of 1  when divided by 2, it is an odd number

the odd multiples of 7 are

7,

21,35,49,63,77

91,105,119,133,147,

161,175, 189, etc

you want one more than a multiple of 5, so it is number ending in 1

answer is 301

the least common multiple of 2,3,4,5,6 is 60

you want a multiple of 60 plus 1 that is also a multiple of 7:301