Final answer:
The LCD of 360 and 3k² is 360.
Step-by-step explanation:
The least common denominator (LCD) of two or more numbers is the smallest number that is a multiple of each of the denominators. To find the LCD of 360 and 3k², we need to factorize 360 and express it in its prime factors, and then incorporate the factors of 3k² that are not already in the factorization of 360.
Let's start by factorizing 360:
Now, let's consider 3k². This expression is already factored, with the prime factor of 3 and the variable part k².
To find the LCD, we take the highest powers of the prime factors from both numbers. Since 360 already includes the factor of 3, we only need to multiply by the variable part that is not in 360's factorization, which is k². Thus, the LCD is 360k², which is option A).
The LCD (Least Common Denominator) of two numbers is the smallest multiple that both numbers have in common. To find the LCD of 360 and 3k², we need to factorize each number into its prime factors.
Prime factorization of 360: 360 = 23 × 32 × 5
Prime factorization of 3k²: 3k² = 3 × k × kThe least common denominator (LCD) of 360 and 3k² is 360k². This is found by factoring both numbers, taking the highest powers of prime factors, and including the variable part k².