College Math Placement Practice Test

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What is the least common multiple (LCM) of 4 and 6?

The correct answer is: 12

To find the least common multiple (LCM) of two numbers, we look for the smallest number that is a multiple of both. For the numbers 4 and 6, we start by identifying their prime factorizations: - The prime factorization of 4 is $2^2$. - The prime factorization of 6 is $2^1 \times 3^1$. To determine the LCM, we take each prime number that appears in the factorizations and use the highest power of that prime. - For the prime number 2, the highest power is $2^2$ (from 4). - For the prime number 3, the highest power is $3^1$ (from 6). Now, we multiply these together to find the LCM: \[ LCM = 2^2 \times 3^1 = 4 \times 3 = 12 \] Thus, the least common multiple of 4 and 6 is 12, which confirms that the solution is indeed correct. The LCM serves as a foundational concept in number theory, particularly useful for adding or subtracting fractions with different denominators, or for solving