HCF stands for Highest Common Factor and it is the largest number that divides two or more numbers completely without leaving any remainder. To find HCF we use methods like prime factorization or division method. It is useful in simplifying fractions solving real-life problems and understanding relationships between numbers and quantities.
Class 10 Maths Chapter 1 focuses on Real Numbers and covers key concepts like Euclid’s Division Lemma irrational numbers and the Fundamental Theorem of Arithmetic. Students will learn to find HCF and LCM using prime factorization and solve problems based on rational and irrational numbers. This chapter prepares students for CBSE Exam 2024-25 and builds a strong foundation in number theory and its applications in mathematics and real-life situations.
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The HCF of two numbers is 18, and their product is 12960. To find their LCM, we use the relationship between HCF and LCM:
HCF × LCM = Product of the two numbers.
Substituting the given values:
18 × LCM = 12960.
Solving for LCM:
LCM = 12960 / 18
LCM = 720.
Thus, the LCM of the two numbers is 720.
Explanation:
The formula HCF × LCM = Product of the numbers is a fundamental property of HCF and LCM. Since the HCF and the product are given, we can directly calculate the LCM using this formula. The other options (420, 600, and 800) do not satisfy this relationship and are therefore incorrect.
Thus, the correct answer is 720.
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