California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

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

The correct answer is: 12

The least common multiple (LCM) of two numbers is the smallest multiple that both numbers share. To find the LCM of 4 and 6, one effective method is to list the multiples of each number. For 4, the multiples are: 4, 8, 12, 16, 20, 24, ... For 6, the multiples are: 6, 12, 18, 24, 30, ... By comparing the lists, the smallest number that appears in both lists is 12. This means that 12 is the first common multiple of both 4 and 6, identifying it as the LCM. Finding the LCM efficiently can also be done using the prime factorization method. The prime factors of 4 are 2 × 2, and for 6, they are 2 × 3. To calculate the LCM, take the highest power of each prime factor appearing in these factorizations. Here, the highest powers are 2 (from 4) and 3 (from 6), resulting in 2² × 3 = 4 × 3 = 12. Therefore, the least common multiple of 4 and