The least common multiple (LCM) of 16 and 24 is 48. The LCM is the smallest number that is a multiple of both 16 and 24. To find the LCM of 16 and 24, there are several methods, including:

• Prime Factorization Method: Find the prime factorization of each number and multiply the highest power of each prime factor together. For 16 and 24, the prime factorization is 16 = 2 x 2 x 2 x 2 and 24 = 2 x 2 x 2 x 3. The highest power of 2 is 2 x 2 x 2 x 2, and the highest power of 3 is 3 x 1. Multiplying these together gives 2 x 2 x 2 x 2 x 3 = 48, which is the LCM.

• Division Method: Divide each number by its prime factors, and then multiply the common prime factors and the remaining factors together. For 16 and 24, the prime factors are 2 and 3. Dividing 16 and 24 by 2 gives 8 and 12, respectively. Dividing 8 by 2 gives 4, and dividing 12 by 2 gives 6. The remaining factors are 2 and 3. Multiplying the common prime factors (2 x 2 x 2) and the remaining factors (3) gives 2 x 2 x 2 x 3 = 48, which is the LCM.

• Listing Multiples Method: List the multiples of each number until you find a common multiple. For 16, the multiples are 16, 32, 48, 64, 80, 96, ... For 24, the multiples are 24, 48, 72, 96, 120, 144, ... The first common multiple is 48, which is the LCM.

Therefore, the LCM of 16 and 24 is 48.