Step 1: Find the prime factorization of each number.
18 can be factored into 2 and 3^2, so its prime factorization is 2^1 * 3^2.
24 can be factored into 2^3 and 3, so its prime factorization is 2^3 * 3^1.
30 can be factored into 2, 3, and 5, so its prime factorization is 2^1 * 3^1 * 5^1.
Step 2: Identify the highest power of each prime number from the factorizations.
The highest power of 2 is 2^3 (from 24).
The highest power of 3 is 3^2 (from 18).
The highest power of 5 is 5^1 (from 30).
Step 3: Multiply these highest powers together to find the L.C.M.
L.C.M. = 2^3 * 3^2 * 5^1.
Step 4: Calculate the multiplication.
2^3 = 8, 3^2 = 9, and 5^1 = 5.
Now multiply: 8 * 9 = 72, and then 72 * 5 = 360.
Step 5: The L.C.M. of 18, 24, and 30 is 360.
Least Common Multiple (L.C.M.) – The L.C.M. of a set of numbers is the smallest number that is a multiple of each of the numbers in the set.
Prime Factorization – Finding the L.C.M. often involves determining the prime factorization of each number to identify the highest powers of all prime factors.
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