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3000 / \ 1000 3 / \ 100 10 / \ / \ 50 2 5 2 / \ 5 10 / \ 2 5
2 x 2 x 2 x 3 x 5 x 5 x 5 = 3000

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To find the least common multiple (LCM) of 2000 and 3000, we first need to find the prime factorization of each number. The prime factorization of 2000 is 2^4 * 5^3, and the prime factorization of 3000 is 2^3 * 3 * 5^3. To find the LCM, we take the highest power of each prime factor that appears in either factorization, which gives us 2^4 * 3 * 5^3 = 6000. Therefore, the LCM of 2000 and 3000 is 6000.


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