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Integer multiples of 48 must be at least as great as 48 and so, if there is more than one, they must add to at least 96.
Since the LCM is 12 then the common multiples are multiples of 12 12, 24, 36, 48
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.
24, 48, 72, 96, 120, 144, 168, 192
24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288.
6, 12, 18, 24, 30, 36, 42, 48, 54, 60.12, 24, 36, 48, 60.15, 30, 45, 60.