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To find the least common multiple (LCM) of two numbers, you first need to find the prime factorization of each number. The prime factorization of 63 is 3^2 x 7, and the prime factorization of 180 is 2^2 x 3^2 x 5. To find the LCM, you take the highest power of each prime factor that appears in either number, which gives you 2^2 x 3^2 x 5 x 7 = 1260. Therefore, the least common multiple of 63 and 180 is 1260.
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