The 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?

This question was previously asked in
SSC GD Previous Paper 7 (Held On: 13 Feb 2019 Shift 1)
View all SSC GD Constable Papers >
  1. 15
  2. 10
  3. 25
  4. 5

Answer (Detailed Solution Below)

Option 4 : 5
Free
SSC GD General Knowledge and Awareness Mock Test
3.4 Lakh Users
20 Questions 40 Marks 10 Mins

Detailed Solution

Download Solution PDF

Concept:

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

Latest SSC GD Constable Updates

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/

Get Free Access Now
Hot Links: teen patti bodhi teen patti apk teen patti gold apk download teen patti game - 3patti poker