Select the correct answerFind the least number when successively divided by 2,3, and 7 it leaves reminder 1,2, and 3 respectively.Options6561756367

The problem is asking for the least number that, when divided by 2, 3, and 7, leaves remainders of 1, 2, and 3, respectively.

To solve this, we can use the Chinese Remainder Theorem.

First, we need to find a number that when divided by 2 leaves a remainder of 1. Any odd number will satisfy this condition.

Next, we need this number to leave a remainder of 2 when divided by 3. This means the number is of the form 3n + 2.

Finally, we need this number to leave a remainder of 3 when divided by 7. This means the number is of the form 7m + 3.

We can start by checking the options given.

Option 1: 656 656 divided by 2 leaves a remainder of 0, so this option is incorrect.

Option 2: 175 175 divided by 2 leaves a remainder of 1, 175 divided by 3 leaves a remainder of 2, and 175 divided by 7 leaves a remainder of 3. So, this option is correct.

Option 3: 63 63 divided by 2 leaves a remainder of 1, but 63 divided by 3 leaves a remainder of 0, so this option is incorrect.

Option 4: 67 67 divided by 2 leaves a remainder of 1, but 67 divided by 3 leaves a remainder of 1, so this option is incorrect.

Therefore, the correct answer is 175.