1. The problem is to find the least common multiple (LCM) of the numbers 3, 2, and 7. 2. The LCM of a set of integers is the smallest positive integer that is divisible by each of the numbers. 3. To find the LCM, we first find the prime factorization of each number: - 3 is prime, so its prime factorization is $3$ - 2 is prime, so its prime factorization is $2$ - 7 is prime, so its prime factorization is $7$ 4. Since all numbers are prime and distinct, the LCM is simply their product: $$\text{LCM} = 3 \times 2 \times 7$$ 5. Calculate the product: $$3 \times 2 = 6$$ $$6 \times 7 = 42$$ 6. Therefore, the least common multiple of 3, 2, and 7 is $42$.