Multiples of a number are found by multiplying that number by the counting numbers.  For example, the multiples of 5 are 5, 10, 15, 20, ... and the multiples of 7 are 7, 14, 21, 28, ...

Just like there is no largest possible counting number, there is no largest multiple of a number.

The least common multiple of 2 or more numbers can be useful.  You probably recognize that when learning to add fractions you found the least common denominator. 

To find the LCM, one method is to list the multiples and pick the smallest one they have in common.  For example:

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

7: 7, 14, 21, 28, 35

You will notice that starting with the smallest of the two numbers is bad strategy.  Start with the bigger number. 

Look at 18 and 5:

18: 18, 36, 54, 72, 90

 5: well, you can just see that 5 goes into numbers that end in 5 or 0, so the answer is 90

You can also find the LCM by prime factorization.  This can be helpful with large composite numbers.

Take 18 and 26.  It would take a while to list the multiples so we'll compare the prime factorizations:

18= 2 * 3 * 3

26 = 2 * 13

The only common prime factor is 2.  Now, multiply all the prime factors but use only one of the pair:

2 * 3 * 3 * 13 = 234

Note that this is the same thing as multiplying the two numbers together and then dividing by their GDF.

18 * 26 ÷2 = 468 ÷2 = 234