Question
Download Solution PDFIf the ratio of two numbers is 17 : 7 and the product of their LCM and their HCF is 119, then the sum of the reciprocals of the LCM and the HCF is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The ratio of two numbers is 17:7.
The product of their LCM and HCF is 119.
Formula used:
Product of two numbers = LCM × HCF
Sum of reciprocals of LCM and HCF = (1/LCM) + (1/HCF)
Calculation:
Let the two numbers be 17x and 7x.
Product of two numbers = 17x × 7x = 119x²
⇒ LCM × HCF = 119
LCM × HCF = Product of two numbers
⇒ 119x² = 119
⇒ x² = 1
⇒ x = 1
⇒ Numbers are 17x = 17 and 7x = 7.
LCM of 17 and 7 = 119
HCF of 17 and 7 = 1
Sum of reciprocals of LCM and HCF = (1/LCM) + (1/HCF)
⇒ Sum = (1/119) + (1/1)
⇒ Sum = 120/119
∴ The correct answer is option (3).
Last updated on Jul 10, 2025
-> RRB NTPC Under Graduate Exam Date 2025 has been released on the official website of the Railway Recruitment Board.
-> The RRB NTPC Admit Card will be released on its official website for RRB NTPC Under Graduate Exam 2025.
-> Candidates who will appear for the RRB NTPC Exam can check their RRB NTPC Time Table 2025 from here.
-> The RRB NTPC 2025 Notification released for a total of 11558 vacancies. A total of 3445 Vacancies have been announced for Undergraduate posts like Commercial Cum Ticket Clerk, Accounts Clerk Cum Typist, Junior Clerk cum Typist & Trains Clerk.
-> A total of 8114 vacancies are announced for Graduate-level posts in the Non-Technical Popular Categories (NTPC) such as Junior Clerk cum Typist, Accounts Clerk cum Typist, Station Master, etc.
-> Prepare for the exam using RRB NTPC Previous Year Papers.
-> Get detailed subject-wise UGC NET Exam Analysis 2025 and UGC NET Question Paper 2025 for shift 1 (25 June) here