List questions from gcd-and-lcm

Published on 18 Jan 2017 - 12:03

574

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Suppose k and l are relatively prime positive integers. What is gcd($k^2 + l^2$, $k + l$)?

Published on 19 Jan 2017 - 1:08

63

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How many solutions are possible

Published on 15 Mar 2026 - 20:12

1.6k

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Lcm and hcf question grade 7

Published on 16 Mar 2026 - 15:25

311

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Prove that the arithmetic progressions intersect if and only if $\gcd(a, b) \mid (s − r)$.

Published on 27 Mar 2026 - 21:56

681

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Proof $\gcd(a,b) = \gcd(a, b +ax)$

Published on 23 Jan 2017 - 14:17

156

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How to avoid getting bogged down in details in proofs?

Published on 23 Jan 2017 - 20:09

113

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$a\times na = LCM(a, b) = b\times nb$. Show that $GCD(na, nb) = 1$.

Published on 16 Mar 2026 - 12:18

92

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Common divisors between three numbers

Published on 30 Jan 2017 - 5:08

798

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Find the greatest number that will divide $2327, 2677, 4007$ and $497$ and will leave a remainder of $17, 37 ,47$ and $57$ respectively.

Published on 30 Jan 2017 - 9:15

223

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Ternary generalizations of $\,\gcd(n,m)\,{\rm lcm}(n,m) = nm$

Published on 16 Mar 2026 - 15:45

338

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Prove $\text{lcm}(x,y)/\text{gcd}(x,y) \in N$

Published on 15 Mar 2026 - 18:34

1.2k

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Sum of all pairs of GCD.

Published on 31 Jan 2017 - 9:10

291

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Prove that $lcm(r,s) = ab$ with a,b coprime, $a|r$ and $b|s$

Published on 01 Feb 2017 - 3:56

31

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Why can $\frac{a}{(a,b)}|(\frac{b}{(a,b)})*(x-y)$ be simplified as $\frac{a}{(a,b)}|(x-y)$?

Published on 01 Feb 2017 - 5:40

List Question

How do you compute the $\gcd(1+n+n^2,1+n+n^2+s+2ns+s^2)$

Suppose k and l are relatively prime positive integers. What is gcd($k^2 + l^2$, $k + l$)?

How many solutions are possible

Lcm and hcf question grade 7

Prove that the arithmetic progressions intersect if and only if $\gcd(a, b) \mid (s − r)$.

Proof $\gcd(a,b) = \gcd(a, b +ax)$

How to avoid getting bogged down in details in proofs?

$a\times na = LCM(a, b) = b\times nb$. Show that $GCD(na, nb) = 1$.

Common divisors between three numbers

Find the greatest number that will divide $2327, 2677, 4007$ and $497$ and will leave a remainder of $17, 37 ,47$ and $57$ respectively.

Ternary generalizations of $\,\gcd(n,m)\,{\rm lcm}(n,m) = nm$

Prove $\text{lcm}(x,y)/\text{gcd}(x,y) \in N$

Sum of all pairs of GCD.

Prove that $lcm(r,s) = ab$ with a,b coprime, $a|r$ and $b|s$

Why can $\frac{a}{(a,b)}|(\frac{b}{(a,b)})*(x-y)$ be simplified as $\frac{a}{(a,b)}|(x-y)$?

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