UPSC CDS I 2025 Mathematics Paper

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