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Answer
The LCM of 24 and 96 is 96.
Solution
To find the least common multiple (LCM) of 24 and 96, you can use the prime factorization method:
1. Prime factorize each number:
24 = 2³ × 3
96 = 2⁵ × 3
2. Identify the highest powers of all prime factors:
For the prime 2, the highest power is 2⁵.
For the prime 3, the highest power is 3¹.
3. Multiply these together:
LCM = 2⁵ × 3 = 32 × 3 = 96
Thus, the LCM of 24 and 96 is 96.
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To find the least common multiple (LCM) of 24 and 96, you can use the prime factorization method. For 24, the prime factorization is \(2^3 \times 3\), and for 96, it’s \(2^5 \times 3\). The LCM takes the highest power of each prime factor found in the numbers. Therefore, the LCM is \(2^5 \times 3^1 = 96\). Voila! The LCM of 24 and 96 is 96. Did you know that the concept of LCM dates back to ancient civilizations like the Babylonians? They used it for trade and astronomy calculations. Even today, LCM finds applications in scheduling problems, such as when planning events that occur at different intervals. It's like a numerical glue that helps you sync everything up!
