# Questions tagged [gcd-and-lcm]

The concepts of *greatest common divisor* (which is also known as *Highest Common Factor*) and *least common multiple* are closely related notions in the integers, and also make sense in certain other rings. The tag is intended to encompass all questions related to these notions.

1,954 questions
Filter by
Sorted by
Tagged with
122 views

43 views

### Special cases when $\deg(\gcd(f,g)) \in \{0,1\}$

Let $k$ be a field of characteristic zero. Let $f=f(t), g=g(t) \in k[t]$ and assume that $\deg(f)=dn$, $\deg(g)=dm$, where $d=\gcd(\deg(f),\deg(g)) \geq 2$, $\gcd(n,m)=1$ and $n < m$. Then we can ...
2k views

### Finding largest 4 digit number divisible by certain numbers.

Okay I am weak in mathematics, I have no shame in saying that. I am preparing for my internals and the concept of the GCD and LCM is quite confusing to me. There is this question which is: Find ...
26 views

27 views

### Prove there exists $2011$ consecutive amazing integers
Recently, I have found this problem: We call a positive integer $n$ amazing if there exists positive integers $a, b, c$ such that the equality n = (b, c)(a, bc) + (c, a)(b, ca) + (a, b)(c, ab)\$...