To find common multiples you first need to break up the numbers into their prime factors. In this case:
4=2x2
9=3x3
12=2x2x3
The next step is to identify common factors and discard the duplicates. Two numbers have two 2s so we can discard two of these. Also, two numbers have a 3, so we can discard 1 of these. That leaves us with 2, 2, 3 and 3. Multiply these together for the LCM:
2x2x3x3 = 36
To find other multiples, you simply multiply the LCM by 1,2,3 etc.
So the first three common multiples are 36, 72 and 108.
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24, 48, 72, 96, 120
8 and 9 are corpime, so their first common multiple is their product. The next common multiples are simply the multiples of that first multiple.The first three common multiples are therefore 72, 144 and 216.
The common multiples of 9 and 16 are 144, 288, 432 and so on.
The common multiples of 3, 4, and 8 are numbers that are divisible by all three of these numbers. To find the common multiples, we first list the multiples of each number: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ... Multiples of 4: 4, 8, 12, 16, 20, 24, ... Multiples of 8: 8, 16, 24, 32, ... The common multiples of 3, 4, and 8 are 24, 48, and so on, as they are the numbers that appear in the lists of multiples of all three numbers.
36, 72, 108 and so on.