What is the least whole number that is divisible by 7, but leaves a remainder of 1 when divided by any integer 2 through 6?
To find the least whole number that is divisible by 7, but leaves a remainder of 1 when divided by any integer 2 through 6, I need to find the smallest positive multiple of 7 that is one more than a common multiple of 2, 3, 4, 5, and 6. The least common multiple of 2, 3, 4, 5, and 6 is 60, since it is the smallest positive number that is divisible by all of them. So I need to find the smallest positive multiple of 7 that is one more than a multiple of 60. I can try adding 1 to multiples of 60 and checking if they are divisible by 7. 60 + 1 = 61, which is not divisible by 7. 120 + 1 = 121, which is also not divisible by 7. 180 + 1 = 181, which is still not divisible by 7. 240 + 1 = 241, which is also not divisible by 7. 300 + 1 = 301, which is divisible by 7, since 301 = 7 * 43. Therefore, 301 is the least whole number that is divisible by 7, but leaves a remainder of 1 when divided by any integer 2 through 6. 