Answer:5^2
Step-by-step explanation:To find the least common multiple (LCM) and greatest common factor (GCF) of two numbers, you'll first want to prime factorize each number and then use the prime factors to calculate the LCM and GCF.
First, let's prime factorize the numbers a and b:
a = 2^3 x 5^2 x 7
b = 3^2 x 5^3 x 11^2
Now, let's calculate the LCM and GCF.
LCM (Least Common Multiple):
To find the LCM, you need to take the highest power of each prime factor that appears in either a or b.
LCM = 2^3 x 3^2 x 5^3 x 7 x 11^2
So, the LCM of a and b is 2^3 x 3^2 x 5^3 x 7 x 11^2.
GCF (Greatest Common Factor):
To find the GCF, you need to take the lowest power of each prime factor that appears in both a and b.
GCF = 5^2
So, the GCF of a and b is 5^2.
In summary:
The LCM of a and b is 2^3 x 3^2 x 5^3 x 7 x 11^2.
The GCF of a and b is 5^2.