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Let $R$ be a nontrivial ring with identity, and let $\mathfrak{A}$, $\mathfrak{B}$ be ideals in $R$.

The Second Isomorphism Theorem for Rings states that $(\mathfrak{A}+\mathfrak{B})/\mathfrak{B}\simeq\mathfrak{A}/(\mathfrak{A}\cap\mathfrak{B})$

For $m, n\ge1$, let $R=\mathbb{Z}$, the ring of integers, and let $\mathfrak{A}=m\mathbb{Z}$, $\mathfrak{B}=n\mathbb{Z}$.

(1) $\mathfrak{A}+\mathfrak{B}$ equals
Select Option GCD$(m, n)\mathbb{Z}$LCM$(m, n)\mathbb{Z}$$mn\mathbb{Z}$
. (2) $\mathfrak{A}\cap\mathfrak{B}$ equals to
Select Option GCD$(m, n)\mathbb{Z}$LCM$(m, n)\mathbb{Z}$$mn\mathbb{Z}$
. (3) $(\mathfrak{A}+\mathfrak{B})/\mathfrak{B}$ equals
Select Option GCD$(m, n)\mathbb{Z}/n\mathbb{Z}$LCM$(m, n)\mathbb{Z}/n\mathbb{Z}$$m\mathbb{Z}$
. (4) $\mathfrak{A}/(\mathfrak{A}\cap\mathfrak{B})$ equals
Select Option $m\mathbb{Z}/$GCD$(m, n)\mathbb{Z}$$m\mathbb{Z}/$LCM$(m, n)\mathbb{Z}$$m\mathbb{Z}/mn\mathbb{Z}$
.
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