Final answer:
The LCM of 360 and 525 is found through prime factorization, taking the highest powers of the prime factors involved. By multiplying these powers together, 25200 is determined to be the least common multiple which is answer option D.
Step-by-step explanation:
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both of the original numbers. To find the LCM of 360 and 525, we can use prime factorization.
First, factor both numbers:
- 360 = 23 × 32 × 5
- 525 = 52 × 3 × 7
To find the LCM, we take the highest power of each prime number from the prime factorization of both numbers:
- 23 (from 360)
- 32 (the higher power between 360 and 525)
- 52 (from 525)
- 7 (from 525)
This results in the LCM being 23 × 32 × 52 × 7 = 360 × 7 = 2520 × 10. Therefore, the correct answer is 25200, which is option D.