Find the LCM of 6a square , 8a , 4ab
The prime factorization of 6a² is 2 × 3 × a × a.
The prime factorization of 8a is 2 × 2 × 2 × a.
The prime factorization of 4ab is 2 × 2 × a × b.
To find the LCM, we need to include all of the unique prime factors with the highest exponent:
2³ × 3 × a² × b = 24a²b
Therefore, the LCM of 6a², 8a, and 4ab is 24a²b.
To find the least common multiple (LCM) of 6a^2, 8a, and 4ab, we need to factorize each term and then take the highest exponent for each prime factor.
Step 1: Factorize 6a^2:
6a^2 = 2 × 3 × a × a
Step 2: Factorize 8a:
8a = 2 × 2 × 2 × a
Step 3: Factorize 4ab:
4ab = 2 × 2 × a × b
Step 4: Find the highest exponent for each prime factor:
The prime factorization for the given terms is:
6a^2 = 2 × 3 × a × a
8a = 2 × 2 × 2 × a
4ab = 2 × 2 × a × b
Taking the highest exponent for each prime factor, we have:
2^3 × 3 × a^2 × b = 8ab^2
Therefore, the LCM of 6a^2, 8a, and 4ab is 8ab^2.