Final answer:
To find the LCM of 24, 36, and 40 using the prime factorization method, expand each number into its prime factors and multiply the highest exponent of each factor.
Step-by-step explanation:
To find the LCM of 24, 36, and 40 using the prime factorization method, we need to expand each number into its prime factors. The prime factorization of 24 is 2^3 * 3^1, the prime factorization of 36 is 2^2 * 3^2, and the prime factorization of 40 is 2^3 * 5^1. Next, we need to take the highest exponent for each prime factor, which gives us 2^3 * 3^2 * 5^1. Multiplying these prime factors together, we get the LCM as 2^3 * 3^2 * 5^1 = 8 * 9 * 5 = 360.
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