Real numbers
Grade Class 10
Question:
<p>If p is prime, then H.C.F. and L.C.M. of p and p + 1 would be</p>
<p style="display:inline">H.C.F. = p(p + 1), L.C.M. = 1</p>
<p style="display:inline">H.C.F. = 1, L.C.M. = p(p + 1)</p>
<p style="display:inline">H.C.F. = p, L.C.M. = p + 1</p>
<p style="display:inline">H.C.F. = p, L.C.M. = p(p + 1)</p>
Step-by-Step Solution
Key Concept: Consecutive integers are always coprime, which implies their H.C.F. is 1 and their L.C.M. is the product of the two numbers.
<p>Since, p is prime<br />
<span class="math-tex">\(\therefore\)</span> p and p + 1 has no common factor other than 1.<br />
<span class="math-tex">\(\therefore\)</span> H.C.F of p and p + 1 = 1<br />
& L.C.M of p and p + 1 = p <span class="math-tex">\(\times\)</span> ( p + 1 ) = p(p + 1)</p>
Correct Answer: B