Question

The prime factor trees for 210 and 357 are shown below. Use the prime factor trees to find the lowest common multiple (LCM) of 210 and 357.

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ZaidProfessional · Tutor for 6 years

Answer

3570

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1. To find the lowest common multiple (LCM) of two numbers using their prime factorizations, we first need to identify the prime factors of each number. 2. The prime factorization of 210 is \(2 \times 3 \times 5 \times 7\). 3. The prime factorization of 357 is \(3 \times 7 \times 17\). 4. To find the LCM, we take the highest power of each prime factor that appears in either number. In this case, the prime factors are 2, 3, 5, 7, and 17. 5. The LCM is then calculated as \(2 \times 3 \times 5 \times 7 \times 17 = 3570\). 6. Therefore, the LCM of 210 and 357 is 3570.

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