The common multiples of 9 and 12 are 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, and so on. They are the infinite set of multiples of the LCM of 9 and 12, which is 36.
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Multiples of 3 include 3, 6, 9, 12, 15, and so on. To be common, they need to be compared to another set of multiples.
There exists infinite common multiples of 9, 12 & 18.But, the least common multiple is only one which can be found by the factorization of each number:PF of 9 = 3x3PF of 12 = 2x2x3PF of 18 = 2x3x3Thus, LCM is 3x3x2x2 = 36Common multiples can be found by multiplying 36(LCM) with 1, 2, 3,...etc.
Common Multiples of 8:8,16,24,32,40,48,56,64,72,80,88 and 96 Common Multiples of 12:12,24,36,48,60,72,84 and 96
Since 36 is a multiple of 12, all of its multiples are common.
To find a number that is not a common multiple of 4 and 9, we need to consider the multiples of each number. The multiples of 4 are 4, 8, 12, 16, 20, 24, ... and the multiples of 9 are 9, 18, 27, 36, 45, ... The first number in the list of multiples of 4 that is not a multiple of 9 is 4. Therefore, 4 is a number that is not a common multiple of 4 and 9.