Answer:
187
Step-by-step explanation:
The desired number will be 7 more than the least common multiple (LCM) of 30, 36, and 45.
30 and 36 have a greatest common factor of 6, so their least common multiple will be 30×36/6 = 180. This is also a multiple of 45, so 180 is the LCM of all three numbers. Seven more than this is 187.
The smallest possible value of m is 187.
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<em>Comment on the answer</em>
Actually, the answer could be m = 180n +7, where n is any integer. If negative values of n are allowed, there is no "smallest", as the numbers tend toward negative infinity. For n=0, m will be 7, which will give the specified remainders. The quotient in each case will be 0, which may not be what you want. The above answer assumes n > 0.
