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**positive integers**##a, b,c## and one unknown ##x## (##x## is also a

**positive integer**). Solve for the

**smallest**##x## that satisfies this equation$$\left \lfloor\frac{x}{a} \right\rfloor + \left \lfloor \frac{x}{b} \right\rfloor \geq c$$

where ##\lfloor x\rfloor## is the [floor function][1]

For instance let ##a = 1##, ##b=1## and ##c=5## in this case

$$\left \lfloor x \right\rfloor + \left \lfloor x \right\rfloor \geq 5$$

here the smallest ##x## is ##3##.

For another case, if ##a=3## and ##b=5## and ##c=4## we obtain

$$\left \lfloor\frac{x}{3} \right\rfloor + \left \lfloor \frac{x}{5} \right\rfloor \geq 4$$

here the smallest ##x## is ##9##

My question is, can we find the smallest ##x## exactly ?

[1]: https://en.wikipedia.org/wiki/Floor_and_ceiling_functions