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

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.

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