Find the LCM for the given numbers using prime factorization.
56 and 96
Prime factors of 56: 2*2*2*7
Prime factors of 96: 2*2*2*2*2*3
The Lowest Common Multiple is the product of five 2's, one 3 and one 7. Multiply that out for the answer.
To find the least common multiple (LCM) of two numbers using prime factorization, follow these steps:
Step 1: Prime factorize each number.
To prime factorize a number, write it as a product of prime factors.
Prime factorization of 56:
56 = 2 * 2 * 2 * 7 = 2^3 * 7
Prime factorization of 96:
96 = 2 * 2 * 2 * 2 * 2 * 3 = 2^5 * 3
Step 2: Identify the common and uncommon factors.
In this case, the common factor is 2, as both numbers have 2 as a prime factor. The uncommon factor for 56 is 7, and for 96 it is 3.
Step 3: Determine the LCM.
To find the LCM, multiply the common factors and the uncommon factors.
LCM = (Common factors) * (Uncommon factors)
LCM = 2 * 2 * 2 * 7 * 3 = 336
Therefore, the LCM of 56 and 96, using prime factorization, is 336.