Question 1: Find the prime factorisation of 36.

Answer: 2^2 * 3^2

Question 2: Find the prime factorisation of 45.

Answer: 3^2 * 5

Question 3: Calculate the LCM of 24 and 36 using the Prime Factor Method.

Answer: 72

Question 4: Determine the LCM of 8, 12, and 20 using prime factorisation.

Answer: 120

Question 5: Explain the steps involved in finding the LCM of 15 and 25 using prime factors.

Answer: Prime factorise both numbers: 15=3*5, 25=5^2. Take the highest powers: 3^1, 5^2. Multiply: 3*25=75.

Question 6: Find the prime factors of 50 and 75 and determine their LCM.

Answer: 150

Question 7: A factory produces 48 and 180 units of two products daily. Find the LCM to determine how often they produce both simultaneously.

Answer: 720

Question 8: Construct the prime factorisation of 84.

Answer: 2^2 * 3 * 7

Question 9: Calculate the LCM of 42 and 70 using their prime factorizations.

Answer: 210

Question 10: Identify and correct the mistake: Find the LCM of 18 and 24 by simply multiplying the numbers.

Answer: Incorrect because it does not account for common factors; the correct LCM is 72.

Question 11: What is the LCM of 20 and 25? Show your prime factorisation process.

Answer: 50

Question 12: Find the LCM of 14, 21, and 28 using prime factors. Is this a common multiple? Why?

Answer: LCM is 84; yes, it is a multiple of all three numbers.