UPSC CDS Math HCF and LCM of Numbers and Polynomials Questions

Given, a,b and c are natural numbers.
1. LCM of (ab,ac)=abc
a×LCM of (b,c)=abc
Hence, statement 1 is correct.
2. HCF of (ab,ac)= Common factor of (ab,ac)=a
and a×HCF(b,c)=a× common
factor of (b,c)=a
Hence, statement 2 is correct.
3. We know that HCF is always less than LCM. Hence, statement 3 is correct.
4. HCF(a,b) divides LCM(a,b) because a common factor
between a,b always divides (a×b).
Hence, statement 4 is correct.