To find the least common multiple (LCM) of the numbers 4, 21, and 24, we can follow these steps:
1. Identify the prime factors of each number:
- Prime factors of 4: [tex]\(4 = 2^2\)[/tex]
- Prime factors of 21: [tex]\(21 = 3 \times 7\)[/tex]
- Prime factors of 24: [tex]\(24 = 2^3 \times 3\)[/tex]
2. Find the highest power of each prime factor that appears in the factorization of any of the numbers:
- For the prime factor 2, the highest power is [tex]\(2^3\)[/tex] (from 24).
- For the prime factor 3, the highest power is [tex]\(3^1\)[/tex] (from both 21 and 24).
- For the prime factor 7, the highest power is [tex]\(7^1\)[/tex] (from 21).
3. Multiply these highest powers together to find the LCM:
- [tex]\(LCM = 2^3 \times 3^1 \times 7^1\)[/tex]
4. Calculate the result:
- [tex]\(2^3 = 8\)[/tex]
- [tex]\(3^1 = 3\)[/tex]
- [tex]\(7^1 = 7\)[/tex]
- Therefore, [tex]\(LCM = 8 \times 3 \times 7 = 24 \times 7 = 168\)[/tex]
So, the least common multiple (LCM) of 4, 21, and 24 is 168.
