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Positive Integers

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If x, y and z are positive integers satisfying 13x=17y=19z, find the minimum value of x+y+z.

Jul 7, 2021

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First we can find the LCM of 13, 17, and 19 which is 4199.

$$x = \frac{4199}{13}\\ y = \frac{4199}{17}\\ z = \frac{4199}{19}$$

You can do the rest from here.

Jul 7, 2021