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i have two questions and i need answers for them

first one:

in the additive group (Z,+)

show that nZ intersection mZ= lZ

, where l is the least common multiple of m and n.

The second question is :

Given H and K two subgroups of a group G , show the following:

(H union K) subgroup of G if and only if H subset of K or K subset of H

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# Show that nZ intersection mZ= lZ

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