Class 10 Maths | Chapter 1 - Real Numbers | L4 - Facts of HCF & LCM | GSEB English Medium 2026 - 27

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Welcome to Lecture 4 of Chapter 1 – Real Numbers
Class 10 Maths | GSEB English Medium | 2026–27
In this lecture, we discuss some important facts and properties related to HCF (Highest Common Factor) and LCM (Least Common Multiple).
Topics Covered:
• Important facts about HCF
• Important facts about LCM
• Relationship between HCF and LCM
• Property: HCF × LCM = Product of the two numbers
• Board exam oriented conceptual understanding
These properties are very important for objective questions and board examination problems.
This video is helpful for:
– GSEB Board Exam 2026–27
– Strengthening Real Numbers concepts
– Solving HCF & LCM based questions
– Quick revision before exams
Make sure to watch previous lectures for complete understanding of Chapter 1 – Real Numbers.
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Content :
Some facts about HCF and LCM
--} The HCF of prime number is always 1.
--} The LCM of prime numbers is always equal to their product.
--} The HCF of two or more numbers is less than or equal to the smallest number.
--} The LCM of two or more numbers is greater than or equal to the largest number.
--} The LCM of numbers is always divisible by their HCF.
--} HCF(a, b) x LCM(a, b) = a x b, Where a and b are natural numbers.

Example 3) Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.
Exercise 1.1) Q. 2) Find the LCM and HCF of the following pairs of integers and verify that HCF x LCM = product of the two numbers
(i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54
Exercise 1.1) Q. 4) Given that HCF(306, 657) = 9, find LCM(306, 657). [June 2021, March 2024]
--} The HCF(17, 23) = 1. [March 2023]
--} H.C.F. of 17, 23 and 29 is 1. [March 2024]
--} HCF(11, 13) = ______. (1, 143, 2) [June 2025]
--} If HCF(12, k) = 6 and LCM(12, k) = 36, then k = _______. [March 2023]
--} The HCF of 17, 23 and 29 by prime factorisation method is [June 2023]
(A) 0 (B) 1 (C) 17 (D) 11339
--} If a, b and c are prime numbers, then their HCF is [March 2019]
(A) a + b + c (B) abc (C) 1 (D) 3
--} HCF(a, b) = 12, then their LCM is not equal to _______. [July 2018]
(A) 24 (B) 36 (C) 48 (D) 40
--} If HCF(96, k) = 4 and LCM(96, k) = 9696, then k = ________. [March 2025]
(A) 96 (B) 440 (C) 404 (D) 4
--} If HCF(x, y) = 1, then HCF(x + y, x - y) = _______. [March 2013]
(A) 1 or 2 (B) x or y (C) x + y or x - y (D) 4
--} If HCF(a, b) = 1, then HCF(a - b, a + b) = _______. [March 2018]
(A) a + b or a - b (B) a or b (C) 1 or 2 (D) 4
--} If p, q and r are prime numbers, then what will be their LCM? [March 2024]
--} The HCF and LCM of two numbers are 9 and 360 respectively, If one number is 45, write the other number? [March 2019]