The largest number which can divide 28 and 42 completely is the HCF of the two numbers.

HCF of 28 and 42
$=2\times 7=14$ 

HCF of two numbers $\times$ LCM of two numbers = Product of the two numbers
$12\times LCM=228$
LCM $=\frac{228}{12}=19$

The smallest number divisible by any 2 or more numbers is their least common multiple (LCM).
The multiples  of 2 : 2 , 4 , 6 , 8 , 10 , 12 , 14 .....
The multiples of 4:  4 , 8 , 12 , 16 , 20 ......
The multiples of 6: 6 , 12 , 18 , 24 .........
As you can see, 12 is the smallest multiple that is commom for all 3 numbers.
So, the LCM of 2, 4, 6 = 12

A number that divides 3 and 6 exactly is a common factor of 3 and 6.
$\therefore$ The greatest number that divides 3 and 6 is equal to their Highest Common Factor (HCF).
We need to find the HCF of 3 and 6.
Factors of 3 = 1 , 3
Factors of 6 = 1 , 2 , 3 , 6
The common factors of 3 and 6 are 1 and 3.
$\therefore$ The highest common factor of 3 and 6 is 3.
$\therefore$The greatest number that divides 3 and 6 exactly is 3.

When 38 is divided by 4, the remainder is 2. So, 4 is not a factor of 38.
When 52 is divided by 6, the remainder is 4. So, 6 is not a factor of 52.
When 33 is divided by 5, the remainder is 3. So, 5 is not a factor of 33.
When 96 is divided by 8 the remainder is 0. So, 8 is a factor of 96.

The LCM of two or more numbers is the least number which is exactly divisible by those numbers.                                                       

Example:  LCM of 4 and 6 is 12. So, 12 is the least number which is exactly divisible by 4 and 6.

One is the common factor for all the numbers.

Each number is divisible by one and the "number itself".

For example, 3 is divisible by both 1 and 3.

Prime numbers are numbers which are divisible by 1 and the "number itself",

So, 3 is a prime number as it is divisible by only 1 and 3.

99 is not a prime number as it is divisible by 1, 9, 11, 99.

98 is also not a prime number as it is divisible by 1, 2, 7, 49, 98.

The largest 2-digit prime number is 97, as it is divisible only by 1 and 97.

He will go to all the 3 classes on the day which is LCM of 6, 12, 18.

LCM $=2\times 3\times 2\times 3=36$
If he attends all the three classes on 1st of April, then he will attend all the three classes after 36 days which is 7th May.