Proving there are $\left\lfloor\frac{n}{\text{lcm}(a,b)}\right\rfloor$ numbers divisible by a and b in [1,n]
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
30639
Efficient computation of $\sum_{k=1}^n \left\lfloor \frac{n}{k}\right\rfloor$
45460
Proof verification of a number theory problem involving sequences.
74523
Proof by Cases involving divisibility
60777
Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$
137016
Showing that $\lfloor\frac{x-1}3\rfloor=\lfloor\frac{x}3+\frac23\rfloor-1$ and $\lfloor\frac{x+1}3\rfloor=\lfloor\frac{x}3+\frac13\rfloor$.
158463
Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$
27449
Product of Divisors of some $n$ proof
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
74809
GCD to LCM of multiple numbers
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
119891
Divisibility and the Fibonacci sequence
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
116970
On the number divisors of a number
82803
Prove that $\lfloor\lfloor x/2 \rfloor / 2 \rfloor = \lfloor x/4 \rfloor$