Finding a Common Factor and Multiple
<p>Given that the highest common factor (HCF) of 20 and p is 10, we have:</p>
<p>Factors of 20: 1, 2, 4, 5, 10, 20. The common factor with p must include 10.</p>
<p>To satisfy the HCF condition, p must include the factor 10. Therefore, p could be 10, 20, or another multiple of 10.</p>
<p>Given that the lowest common multiple (LCM) of 20 and p is 60, we calculate:</p>
<p>LCM(20, p) = (20 * p) / HCF(20, p)</p>
<p>Setting the equation for LCM:</p>
<p>(20 * p) / 10 = 60</p>
<p>20p = 600</p>
<p>p = 30</p>
<p>The smallest possible value of p is therefore:</p>
<p>p = 30</p>
