Find the LCM for the given numbers using prime factorization.
8) 56 and 96
Start by finding prime factors:
56 --> 7*8 --> 7*2^3
96 --> 6*16 --> 3*2^5
Just keep dividing by any factors until you get prime factors.
Now, you need to multiply 7*3*2^5 to include all factors. 7*3*2^5 = 672
To find the LCM (Least Common Multiple) of two numbers using prime factorization, you need to follow these steps:
Step 1: Find the prime factorization of each number.
- Prime factorization of 56: 2 * 2 * 2 * 7
- Prime factorization of 96: 2 * 2 * 2 * 2 * 2 * 3
Step 2: Identify all the unique prime factors.
- Unique prime factors: 2, 7, and 3
Step 3: Take the highest power of each prime factor from the two factorizations.
- Highest power of 2: 2^4 (from 96)
- Highest power of 7: 7^1 (from 56)
- Highest power of 3: 3^1 (from 96)
Step 4: Multiply all the highest powers together.
2^4 * 7^1 * 3^1 = 2^4 * 7 * 3 = 16 * 7 * 3 = 336
Therefore, the LCM of 56 and 96 using prime factorization is 336.