Answer :
Final answer:
The least number that leaves a remainder of 3 when divided by 24, 36, 45, and 54 is 360.
Explanation:
To find the least number that leaves a remainder of 3 when divided by 24, 36, 45, and 54, we need to find the least common multiple (LCM) of these numbers.
Step 1: Find the prime factorization of each number: 24 = 2^3 * 3, 36 = 2^2 * 3^2, 45 = 3^2 * 5, and 54 = 2 * 3^3.
Step 2: Take the highest power of each prime factor that appears in any of the numbers. In this case, we need 2^3, 3^3, and 5^1.
Step 3: Multiply these prime factors together: LCM = 2^3 * 3^3 * 5 = 360.
Therefore, the least number that leaves a remainder of 3 when divided by 24, 36, 45, and 54 is 360.
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