A multiple of 6 would be any number that 6 divides into evenly (meaning no remainder). Between 4 and 50 these numbers would be 6, 12, 18, 24, 30, 36, 42, and 48.
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Look at the multiples of 6. The smallest and greatest multiples of 6 that can be divided evenly by 4 are 12 and 48. So the common multiples of 4 and 6 up to 50 are 12, 24, 36, and 48.
Since the LCM is 12 then the common multiples are multiples of 12 12, 24, 36, 48
The multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76 and so on. The multiples of 6 are 6,12,18,24,30,36,42,48,52,58,62,66,72,78,84,90,96,102 and so on.
They are: 6 12 18 24 30 36 42 and 48
The possibilities are 2, 4 and 6 which are all multiples of two. So the odds are 50:50