Question
Download Solution PDFThe Least Common Multiple and Highest common Factor of two numbers are 30 and 5 respectively. If their sum is 25, then what will be the difference of these two numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The largest common factor of two or more numbers is called the highest common factor.
The smallest positive number that is a multiple of two or more numbers is called Least common multiple
Formula Used:
LCM × HCF = Product of two number
Calculation:
Let the number be a and b
LCM × HCF = a × b
⇒ a × b = 150 ---- (1)
Given than,
⇒ a + b = 25 ----(2)
Taking square on both sides,
⇒ (a + b)2 = 252
⇒ a2 + b2 + 2ab = 625
⇒ a2 + b2 + 2(150) = 625
⇒ a2 + b2 = 625 – 300 = 325 ----(3)
(a – b)2 = a2 + b2 – 2ab
⇒ (a – b)2 = 325 – 2(150)
⇒ (a – b)2 = 325 – 300 = 25
⇒ a – b = 5 ----(4)
Adding equation (2) and (4),we get,
⇒ a + b + a – b = 25 + 5
⇒ 2a = 30
⇒ a = 30/2 = 15
Substituting a = 15, in equation (4)
⇒ a – b = 5,
⇒ 15 – b = 5
⇒ b = 15 – 5 = 10
∴ required difference of these two numbers = 15 – 10 = 5
Last updated on Jun 6, 2025
-> The SSC GD Notification 2026 will be released in October 2025 and the exam will be scheduled in the month of January and February 2026.
-> The SSC GD Merit List is expected to be released soon by the end of April 2025.
-> Previously SSC GD Vacancy was increased for Constable(GD) in CAPFs, SSF, Rifleman (GD) in Assam Rifles and Sepoy in NCB Examination, 2025.
-> Now the total number of vacancy is 53,690. Previously, SSC GD 2025 Notification was released for 39481 Vacancies.
-> The SSC GD Constable written exam was held on 4th, 5th, 6th, 7th, 10th, 11th, 12th, 13th, 17th, 18th, 19th, 20th, 21st and 25th February 2025.
-> The selection process includes CBT, PET/PST, Medical Examination, and Document Verification.
-> The candidates who will be appearing for the 2025 cycle in the exam must attempt the SSC GD Constable Previous Year Papers. Also, attempt SSC GD Constable Mock Tests.
-> UPSC Prelims Result 2025 Date Out soon @https://upsconline.nic.in/