Real numbers
Grade Class 10
Question:
<p><strong>Assertion (A):</strong> For any two positive integers a and b, HCF(a, b) <span class="math-tex">\(\times\)</span> LCM(a, b) = a <span class="math-tex">\(\times\)</span> b<br />
<strong>Reason (R):</strong> The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.</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: For any two positive integers, the product of their HCF and LCM is always equal to the product of the numbers themselves.
<p>We have,<br />
LCM(a, b) <span class="math-tex">\(\times\)</span> HCF(a, b) = a <span class="math-tex">\(\times\)</span> b<br />
LCM <span class="math-tex">\(\times\)</span> 5 = 150<br />
LCM = <span class="math-tex">\(\frac{150}{5}\)</span> = 30<br />
LCM = 30</p>
Correct Answer: C