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Fungrim entry: fbe121

lcm ⁣(rs,c)=lcm ⁣(r,c)lcm ⁣(s,c)c\operatorname{lcm}\!\left(r s, c\right) = \frac{\operatorname{lcm}\!\left(r, c\right) \operatorname{lcm}\!\left(s, c\right)}{\left|c\right|}
Assumptions:rZ  and  sZ  and  cZ  and  gcd ⁣(r,s)=1  and  c0r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1 \;\mathbin{\operatorname{and}}\; c \ne 0
\operatorname{lcm}\!\left(r s, c\right) = \frac{\operatorname{lcm}\!\left(r, c\right) \operatorname{lcm}\!\left(s, c\right)}{\left|c\right|}

r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1 \;\mathbin{\operatorname{and}}\; c \ne 0
Fungrim symbol Notation Short description
LCMlcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
Absz\left|z\right| Absolute value
ZZZ\mathbb{Z} Integers
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Source code for this entry:
    Formula(Equal(LCM(Mul(r, s), c), Div(Mul(LCM(r, c), LCM(s, c)), Abs(c)))),
    Variables(r, s, c),
    Assumptions(And(Element(r, ZZ), Element(s, ZZ), Element(c, ZZ), Equal(GCD(r, s), 1), NotEqual(c, 0))))

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2021-03-15 19:12:00.328586 UTC