Final Answer:
The least common multiple (LCM) of 9 and 6 is 18. This is found by identifying their prime factors (9 = 3², 6 = 2 × 3) and taking the highest power of each prime factor appearing in either number.
Step-by-step explanation:
To find the least common multiple (LCM) of 9 and 6, we'll use the method of prime factorization. First, break down both numbers into their prime factors. For 9, the prime factorization is 3² (as 3 × 3 = 9), and for 6, it's 2 × 3. The LCM is calculated by taking the highest power of each prime factor that appears in either number. In this case, the LCM of 9 and 6 would be 2¹ × 3², which equals 18. Therefore, 18 is the smallest multiple that both 9 and 6 share, making it their least common multiple.
Understanding the concept of prime factorization is crucial in finding the LCM of numbers. By breaking down the numbers into their prime factors and identifying the highest powers of these factors present in any of the numbers, we can determine the least common multiple. In this case, the prime factors of 9 (3²) and 6 (2 × 3) help us ascertain that 18 is the smallest number that is a multiple of both 9 and 6.
The LCM is used in various mathematical problems, especially in situations involving fractions, simplifying expressions, and finding common denominators. Knowing how to calculate the LCM allows for efficient problem-solving and helps in finding the smallest common multiple among given numbers.