Real numbers
Grade Class 10
Question:
<p>The least positive integer divisible by 20 and 24 is</p>
<p style="display:inline">240</p>
<p style="display:inline">360</p>
<p style="display:inline">120</p>
<p style="display:inline">480</p>
Step-by-Step Solution
Key Concept: The smallest positive integer divisible by a set of numbers is their Least Common Multiple (LCM), which is the product of the highest powers of all prime factors present in those numbers.
<p>Least positive integer divisible by 20 and 24 is<br />
LCM of (20, 24).<br />
20 = 2<sup>2</sup> <span class="math-tex">\(\times\)</span> 5<br />
24 = 2<sup>3</sup> <span class="math-tex">\(\times\)</span> 3<br />
<span class="math-tex">\(\therefore \)</span> LCM (20, 24) = 2<sup>3</sup> <span class="math-tex">\(\times\)</span> 3 <span class="math-tex">\(\times\)</span> 5 = 120<br />
Thus 120 is divisible by 20 and 24.</p>
Correct Answer: C