The gcd of two numbers is 17 and their lcm is 204. one of the numbers is 68. find the other number.

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16-05-2018
Mathematics

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The gcd of two numbers is 17 and their lcm is 204. one of the numbers is 68. find the other number.

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gmany gmany · Answer 1 · 2019-01-03T21:09:24+01:00

gmany gmany

03-01-2019

[tex]x\cdot y=GCD(x,\ y)\cdot LCM(x,\ y)\\\\\text{We have}\\\\x=68,\ GCD=17,\ LCM=204.\\\\\text{Substitute:}\\\\68y=(17)(204)\\\\68y=3,468\qquad\text{divide both sides by 68}\\\\\boxed{y=51}\\\\Answer:\ \boxed{\text{The other number is 51.}}[/tex]

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