If the LCM of two numbers is 180 and their HCF is 15, what is the sum of the two

If the LCM of two numbers is 180 and their HCF is 15, what is the sum of the two numbers? (2023)

If the LCM of two numbers is 180 and their HCF is 15, what is the sum of the two numbers? (2023)

Step 1: Understand that LCM (Least Common Multiple) and HCF (Highest Common Factor) are related to two numbers.
Step 2: Let the two numbers be represented as 15a and 15b, where 15 is their HCF.
Step 3: Since the LCM of the two numbers is given as 180, we can use the formula: LCM = HCF * (a * b).
Step 4: Substitute the known values into the formula: 180 = 15 * (a * b).
Step 5: Simplify the equation: a * b = 180 / 15, which gives a * b = 12.
Step 6: Now, find pairs of numbers (a, b) that multiply to 12. The pairs are (1, 12), (2, 6), (3, 4).
Step 7: Calculate the actual numbers using the pairs: For (3, 4), the numbers are 15*3 = 45 and 15*4 = 60.
Step 8: Add the two numbers together: 45 + 60 = 105.

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