Question 1: Find the prime factorization of 56.

Answer: 2^3 * 7

Question 2: Find the prime factorization of 90.

Answer: 2 * 3^2 * 5

Question 3: Calculate the LCM of 48 and 180 using the Prime Factor Method.

Answer: 720

Question 4: Determine the LCM of 24, 36, and 60 by prime factorization.

Answer: 360

Question 5: Explain why the prime factorization method guarantees finding the LCM of two numbers.

Answer: Because the LCM is found by taking the highest powers of all primes involved, ensuring the multiple is divisible by both numbers.

Question 6: The numbers 84 and 126 are both divisible by 3. Find their LCM using prime factors and verify your answer by listing multiples.

Answer: LCM = 420; multiples include 84, 126, 420, etc.

Question 7: Calculate the LCM of 105 and 140 using prime factorization. Show each step.

Answer: LCM = 420

Question 8: A school schedules events every 12 days and every 15 days. When will both events occur on the same day? Find the answer using the Prime Factor Method.

Answer: LCM = 60 days

Question 9: Find the LCM of 72 and 108, then explain the prime factorization process you used.

Answer: LCM = 216; prime factors are 2^3 * 3^3

Question 10: Identify and correct the mistake in this prime factorization for 84: 2^2 * 3 * 7.

Answer: The correct factorization is 2^2 * 3 * 7; the given is correct, so no mistake.

Question 11: Construct a set of three numbers with different prime factors and find their LCM using prime factorization. Justify your choices.

Answer: Example: 20, 35, 42; LCM = 420; justified by prime factors.