The sum of two numbers is 36 and the HCF and LCM of these numbers are 3 and 105 respectively. Find the sum of their reciprocals.
Answer & explanation
Correct answer: option 3
Product of other factors = \(\frac{LCM}{HCF}\) = \(\frac{105}{3}\) = 35
Sum of other factors = \(\frac{Sum\;of\;numbers}{HCF}\) = \(\frac{36}{3}\) = 12
Then, only 7, 5 satisfy the condition.
Numbers are: -
7 × 3 = 21
5 × 3 = 15
Reciprocal of numbers = \(\frac{1}{21}\) + \(\frac{1}{15}\) = \(\frac{5 + 7}{105}\) = \(\frac{12}{105}\) = \(\frac{4}{35}\)