Proving lcm(m,n)=k using mZ and nZ intersection

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Homework Statement


prove:mZ\cap nZ=kZ
where lcm(m,n)=k

Homework Equations


The Attempt at a Solution


i can prove that kZ is a subset of mZ and nZ but i cannot prove further!
thx for ur help!
 
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If x in mZ and nZ, x = am = bn for some integers a and b. So x is a common multiple of m and n. What is the relationship of x to k?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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