Approximate while you can

Given that $$m$$ and $$n$$ are natural numbers and among all possible rational numbers with the restriction $$(m + n) < 150$$, $$\frac{m}{n}$$ is the best approximation of $$\sqrt{14}$$ then what is $$n$$?

Use: $$\sqrt{14} = 3.741657387. . .$$

×