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If we have two functions $f:\mathbb{R} \to \mathbb{R}$ and $g :\mathbb{R} \to \mathbb{R}$ such that the period of $f$ is 7 and that of $g$ is 11, then the period of $F\left ( x \right ) = f( x)g(\frac{x}{5}) + g(x)f(\frac{x}{3})$ is ?

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Since you are new, I want to give you some advice about the site: To get the best possible answers, you should explain what your thoughts on the problem are so far. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people are much more willing to help you if you show that you've tried the problem yourself. –  Zev Chonoles Dec 21 '12 at 5:39
    
Hint: How does multiplying your input $x$ by a constant $k$ change the periodocity? –  Rustyn Dec 21 '12 at 8:21
    
@ZevChonoles See, I know that probably the product of two functions probably has a period equal to the L.C.M. of their individual periods. Same for the sum. The only problem was verifying the procedure and the answer. –  wamiq reyaz Dec 22 '12 at 16:53

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