LCM of two numbers is odd only if both numbers are odd Among prime numbers, 2 is the only even prime Calculation: If p=2,q=3⇒LCM=6 (even) So, LCM is not always odd Statement I is incorrect Statement II: Sum of their LCM and HCF is always even HCF of two distinct primes =1 LCM of p and q=p×q Sum =p×q+1 Check: p=2,q=3⇒LCM=6,HCF=1⇒ Sum = 6+1=7 odd p=3,q=5⇒LCM=15,HCF=1⇒ Sum =15+1=16 even p=3,q=7⇒21+1=22 even
But counter example: p=2,q=3⇒6+1=7 Statement II is incorrect
