Real numbers
Grade Class 10
Question:
<p>If two positive integers ‘a’ and ‘b’ are written as <span class="math-tex">\(a = p{q^2}\)</span> and <span class="math-tex">\(b = {p^3}{q^2}\)</span>, where ‘p’ and ‘q’ are prime numbers, then LCM(a, b) =</p>
<p style="display:inline">p<sup>2</sup>q<sup>2</sup></p>
<p style="display:inline"><span class="math-tex">\({p^3}{q^2}\)</span></p>
<p style="display:inline">p<sup>2</sup>q<sup>3</sup></p>
<p style="display:inline">pq</p>
Step-by-Step Solution
Key Concept: The LCM of numbers expressed in prime factorization form is the product of the highest power of each prime factor present in any of the numbers.
<p>We know that LCM = product of the highest powers of all the prime factors of the numbers pq<sup>2</sup>, p<sup>3</sup>q<sup>2</sup> <br />
LCM = p<sup>3</sup>q<sup>2</sup></p>
Correct Answer: B