To find the least number that satisfies the given conditions, we need to find the least common multiple (LCM) of 16, 18, and 20.

Finding LCM of 16, 18, and 20:
To find the LCM, we can start by finding the prime factors of each number:

16 = 2^4
18 = 2 * 3^2
20 = 2^2 * 5

Next, we take the highest power of each prime factor:

2^4 * 3^2 * 5 = 720

Therefore, the LCM of 16, 18, and 20 is 720.

Finding the number that satisfies the given conditions:
Now, we know that the number we are looking for should leave a remainder of 4 when divided by 16, 18, and 20.

This means that the number must be of the form:
720k + 4, where k is an integer.

To find the least number that is completely divisible by 7, we can start by finding the remainder when 720 is divided by 7:

720 ÷ 7 = 102 remainder 6

Next, we need to add a multiple of 720 to 6 so that the sum is divisible by 7:

6 + 720 = 726
726 ÷ 7 = 103 remainder 5

We can see that adding 720 to 6 gives us a remainder of 5 when divided by 7. We need to find the next multiple of 720 that gives a remainder of 5 when divided by 7:

103 * 720 = 74160
74160 ÷ 7 = 10594 remainder 2

Adding another multiple of 720 to 74160:

74160 + 720 = 74880
74880 ÷ 7 = 10697 remainder 1

We can see that adding 720 to 74160 gives us a remainder of 1 when divided by 7. We need to find the next multiple of 720 that gives a remainder of 1 when divided by 7:

10697 * 720 = 7701840
7701840 ÷ 7 = 1100262 remainder 6

Adding another multiple of 720 to 7701840:

7701840 + 720 = 7702560
7702560 ÷ 7 = 1100366 remainder 2

Finally, we can see that adding 720 to 7701840 gives us a remainder of 2 when divided by 7.

Therefore, the least number that satisfies the given conditions is:
7701840 + 720 = 7702560

So the correct answer is option 'D', 7702560.