Real numbers
Grade Class 10
Question:
<p><strong>Assertion (A): </strong>For any two natural numbers a and b, the HCF of a and b is a factor of the LCM of <span class="math-tex">\(a\)</span> and <span class="math-tex">\(b\)</span>.<br />
<strong>Reason (R): </strong>HCF of any two natural numbers divides both the numbers.</p>
<p style="display:inline">Both A and R are true and R is the correct explanation of A.</p>
<p style="display:inline">Both A and R are true but R is not the correct explanation of A.</p>
<p style="display:inline">A is true but R is false.</p>
<p style="display:inline">A is false but R is true.</p>
Step-by-Step Solution
Key Concept: The HCF of two numbers is a factor of their LCM because the HCF divides the numbers, and any divisor of the numbers must also divide their common multiples due to the transitive property of divisibility.
<p>Both A and R are true and R is the correct explanation of A.</p>
Correct Answer: A