Find the LCM and HCF of the following integers by applying the prime factorization method:
(i) 12, 15 and 21
(ii) 17, 23 and 29
(iii) 8, 9 and 25
Ex 1.2 Class 10 Maths Question 4:
Given that HCF (306, 657) = 9, find LCM (306, 657).
Ex 1.2 Class 10 Maths Question 5.
Check whether 6n can end with the digit 0 for any natural number n.
Ex 1.2 Class 10 Maths Question 6.
Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
Ex 1.2 Class 10 Maths Question 7.
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point?
Solution:
CBSE Class 10 Real Numbers — Complete Guide
Real Numbers is the foundation chapter of CBSE Class 10 Mathematics, carrying approximately 6 marks in the board exam. This chapter covers Euclid's division algorithm, the Fundamental Theorem of Arithmetic, irrational number proofs, and decimal expansions of rational numbers.
Quick Revision: Key Concepts
- Euclid's Division Lemma: a = bq + r (0 ≤ r < b) — used to find HCF
- Fundamental Theorem: Every composite number = unique product of primes
- HCF: Common primes with smallest powers | LCM: All primes with greatest powers
- HCF × LCM = Product of two numbers
- Irrationality: √2, √3, √5 are irrational (proof by contradiction)
- Terminating decimals: p/q terminates iff q = 2m × 5n
Board Exam Pattern
Typically 2-3 MCQs (1 mark each) on HCF/LCM and decimal expansions, plus 1 short answer question (2-3 marks) on irrationality proof or Euclid's algorithm. Total: approximately 6 marks.
Most Important Questions
- Find HCF using Euclid's algorithm
- Find HCF and LCM using prime factorisation and verify HCF × LCM = product
- Prove √2 (or √3 or √5) is irrational
- Determine if decimal expansion is terminating or non-terminating
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