‘K’ is divisible by 3, 4, and 5. Try and answer the following questions to infer what kind of number K is. That should help you get to the solution to this question.

1. If a number K is divisible by another number d, will K be a multiple of d?
2. Is K the only such number or are there other numbers that will also be divisible by d?
3. If K is divisible by d, e, and f will it be a multiple of all three numbers?
4. What numbers, other than K, will also be divisible by all three numbers d, e, and f?

Step 1: What is the least value of K that will be divisible by 3, 4, and 5?

If K is divisible by 3, 4, and 5, K has to be a multiple of 3, 4, and 5.

i.e., K is a common multiple of 3, 4, and 5.

The smallest or the first multiple common to 3, 4, and 5 is the LCM of 3, 4, and 5.

So, let us find the LCM of 3, 4, and 5.

Step 1: Prime factorize all the numbers.
3 is a prime number. 5 is also a prime number. When prime factorized, 4 will be written as 2².

Step 2: Write down all the prime factors in their respective highest power.
3, 2² and 5

Step 3: The LCM is the product of all different prime factors found in these numbers in their respective highest powers.
So, LCM of 3, 4 and 5 = 3 * 2² * 5 = 60.

So, K will be 60 or any multiple thereof.

Take a quick look at the choices to determine which of the three sets of numbers will also divide K to get the answer.

Step 2: Check which of the choices divides 60

Option I: 3, 4, and 15
All these numbers will divide 60. So, Option I will be a part of the answer.

Option II: 12, 15, and 18
12 and 15 will divide 60. However, 18 will not. So, Option II is not correct.

Option III: 5, 20, and 30
All these numbers will divide 60. So, Option III will be a part of the answer.

  Hence, the correct answer is Choice D – I and III only.