## Elementary Algebra

$462$
Factor each number completely to obtain: $42= 2\cdot 3\cdot 7 \\66 = 2 \cdot 3 \cdot 11$ The different factors that appear in the prime factorization of the given numbers are 2, 3, 7, and 11. The maximum number of times that each unique factor appears in the factorization is: For 2: once For 3: once For 7: once For 11: once The least common multiple will have one 2, one 3, one 7, and one 11. Thus, the least common multiple of the given numbers is: $=2 \cdot 3\cdot 7 \cdot 11 \\= 462$