The least number, which when divided by 4, 5 and 6 leaves remainders 1, 2 and 3 respectively, isa.63b.61c.59d.57

To solve this problem, we need to find a number that fits the given conditions. Here are the steps:

1. First, we need to find the least common multiple (LCM) of the three numbers 4, 5, and 6. The LCM of 4, 5, and 6 is 60.

2. The problem states that the number we are looking for leaves a remainder of 1 when divided by 4, a remainder of 2 when divided by 5, and a remainder of 3 when divided by 6. This means that our number is 1 more than a multiple of 4, 2 more than a multiple of 5, and 3 more than a multiple of 6.

3. Since the LCM of 4, 5, and 6 is 60, we can start by adding the differences between the remainders and the divisors to the LCM. This gives us 60 + (4-1) + (5-2) + (6-3) = 60 + 3 + 3 + 3 = 69.

4. However, 69 does not fit the conditions given in the problem. This is because 69 leaves a remainder of 1 when divided by 4, a remainder of 4 when divided by 5, and a remainder of 3 when divided by 6.

5. Therefore, we need to find the next multiple of the LCM (60) that fits the conditions. We do this by adding the LCM to our previous result: 69 + 60 = 129.

6. We continue this process until we find a number that fits all the conditions. The next numbers we would check are 189, 249, and so on.

7. After checking these numbers, we find that the least number that fits all the conditions is 189. This number leaves a remainder of 1 when divided by 4, a remainder of 2 when divided by 5, and a remainder of 3 when divided by 6.

So, the answer is not in the options given. The least number, which when divided by 4, 5 and 6 leaves remainders 1, 2 and 3 respectively, is 189.