Question
Download Solution PDFThree numbers x ≤ y ≤ z which are co-prime to each other are such that the product of the first two numbers is 143 and that of the last two numbers is 195. The sum of the three numbers is ______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Product of first two numbers = 143
Product of last two numbers = 195
Concept used:
Numbers are co-prime when the only common factor that they have is 1.
HCF = 1
Calculations:
Let the numbers be a, b, and c
⇒ x × y = 143, y × z = 195
These two products have y as common.
HCF of 143 and 195 = y = 13
⇒ a = 143/13 = 11
⇒ b = 195/13 = 15
∴ The three co-prime numbers are 11, 13, and 15.
Sum = 11 + 13 + 15 = 39
The answer is 39.
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