Final answer:
The least common multiple (LCM) of 10 and 36 is determined to find out when Brenda will next cut her grass and trim her shrubs on the same day, which is 180 days from June 1, making D. 180 days the correct answer.
Step-by-step explanation:
The student is asking how many days will pass before Brenda cuts her grass and trims her shrubs on the same day again if she cuts her grass every 10 days and trims her shrubs every 36 days, having done both on June 1. To find the number of days before both activities coincide again, we need to calculate the least common multiple (LCM) of the two periods: 10 and 36.
The prime factorization of 10 is 2 × 5, and of 36 is 2² × 3². The LCM is obtained by taking the highest powers of all prime factors that appear in the factorization of both numbers. Therefore, LCM(10, 36) = 2² × 3² × 5 = 4 × 9 × 5 = 36 × 5 = 180.
So, Brenda will cut her grass and trim her shrubs on the same day 180 days after June 1. The correct answer is D. 180 days.