The LCM of two numbers is 84 and their HCF is 12. What is the sum of the two num

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Question: The LCM of two numbers is 84 and their HCF is 12. What is the sum of the two numbers if they are both less than 100? (2023)

Options:

Correct Answer: 72

Exam Year: 2023

Solution:

Let the two numbers be 12a and 12b. Then, 12ab = 84, so ab = 7. The pairs (1, 7) and (7, 1) give us 12 and 84, which sum to 96.

The LCM of two numbers is 84 and their HCF is 12. What is the sum of the two numbers if they are both less than 100? (2023)

The LCM of two numbers is 84 and their HCF is 12. What is the sum of the two numbers if they are both less than 100? (2023)

Step 1: Understand that the LCM (Least Common Multiple) of two numbers is 84 and their HCF (Highest Common Factor) is 12.
Step 2: Let the two numbers be represented as 12a and 12b, where 'a' and 'b' are integers.
Step 3: Use the relationship between LCM, HCF, and the two numbers: LCM = HCF * (a * b).
Step 4: Substitute the known values into the equation: 84 = 12 * (a * b).
Step 5: Simplify the equation: a * b = 84 / 12, which gives a * b = 7.
Step 6: Find pairs of integers (a, b) that multiply to 7. The pairs are (1, 7) and (7, 1).
Step 7: Calculate the two numbers using the pairs: For (1, 7), the numbers are 12*1 = 12 and 12*7 = 84.
Step 8: Add the two numbers together: 12 + 84 = 96.
Step 9: Verify that both numbers (12 and 84) are less than 100, which they are.

LCM and HCF Relationship – The relationship between the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers, which states that the product of the two numbers is equal to the product of their LCM and HCF.
Factorization – Understanding how to express numbers in terms of their factors, particularly in relation to the HCF.
Sum of Numbers – Calculating the sum of two numbers based on their derived values from LCM and HCF.