The least common multiple of the integers a1a2, …, an, which are not all zero, is the smallest positive integer that is divisible by all the integers a1, a2,…, an; it is¡ denoted by [a1,a2,…, an].
a) Show that if a, b, and c are integers, then [a,b]| c if and only if a | c and b | c.
b) Show that if a1, a2, …, an and d are integers where n is a positive integer, then [a1, a2, …, an] | d if and only if ai | d for i = 1, 2, …, n.
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