Final answer:
The LCM of 35 and 100 is 700 minutes, which is found by taking the highest powers of each prime from the prime factorization of these numbers. There appears to be a mistake in the provided multiple-choice answers, as none correspond to the correct LCM.
Step-by-step explanation:
The least common multiple (LCM) of two numbers is the smallest positive integer which is a multiple of both numbers. To find the LCM of 35 and 100, we can list the multiples of each number until we find a common one.
While doing this, we observe that 35 and 100 do not have a common multiple within the smaller numbers. We see that 35 is a multiple of 5 and 7, and 100 is a multiple of 5, 2, and 10.
The prime factorization of 35 is 5 * 7, and for 100, it is 22 * 52. We take the highest powers of each prime that appear in the factorizations of both numbers, which are 22, 52, and 7. Therefore, LCM(35, 100) = 22 * 52 * 7 = 4 * 25 * 7 = 700. So, the LCM of 35 and 100 is 700 minutes.
Reviewing the multiple choice options, there is no option for 700 minutes, which suggests there may be a mistake in the options provided, as none of them represent the correct LCM of 35 and 100.