← Topic 2 · Number Theory
AMC 10/12 · Cheatsheet
Topic 2 · Number Theory
Chapter 2 · Primes, GCD/LCM & bases
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GCD / LCM
gcd
:
min
exps
,
lcm
:
max
exps
\gcd: \min\text{ exps},\;\; \operatorname{lcm}: \max\text{ exps}
g
cd
:
min
exps
,
lcm
:
max
exps
Product identity
gcd
(
a
,
b
)
⋅
lcm
(
a
,
b
)
=
a
b
\gcd(a,b)\cdot\operatorname{lcm}(a,b)=ab
g
cd
(
a
,
b
)
⋅
lcm
(
a
,
b
)
=
ab
Base = polynomial
d
k
⋯
d
0
‾
b
=
∑
d
i
b
i
\overline{d_k\cdots d_0}_b = \sum d_i b^i
d
k
⋯
d
0
b
=
∑
d
i
b
i
Digit-sum (mod 9)
n
≡
n \equiv
n
≡
digit sum
(
m
o
d
9
)
\pmod 9
(
mod
9
)
since
10
i
≡
1
10^i\equiv1
1
0
i
≡
1
.