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 = 3x3
PF of 12 = 2x2x3
PF of 18 = 2x3x3
Thus, LCM is 3x3x2x2 = 36
Common multiples can be found by multiplying 36(LCM) with 1, 2, 3,...etc.
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The LCM of 9, 12, and 18 is 36. Additional common multiples are 72, 108, 144, 180, etc.
For 9: 9, 18, 27, 36 and so on. For 12: 12, 24, 36, 48 and so on. For 18: 18, 36, 54, 72 and so on. Common multiples include, 36, 72, 108, 144 and so on.
The common multiples of 6 and 9 are the infinite set of multiples of their LCM, which is 18. So the common multiples of 6 and 9 are 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, and so on.
To find the common multiples of 2, 3, and 9, we first need to list out the multiples of each number. The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, and so on. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, and so on. The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, and so on. The first three common multiples of 2, 3, and 9 are 18, 36, and 54.
The first 5 multiples of 9 are 9, 18, 27, 36, and 45. For them to be common, they need to be compared to another set of multiples.
Oh, what a happy little question! When we talk about multiples, we're looking at numbers that both 2 and 9 can be divided into evenly. The common multiples of 2 and 9 are numbers like 18, 36, 54, and so on - just like little friends skipping along together in the meadow.