Question

Can two numbers have 16 as their H.C.F and 380 as their L.C.M.? Give reason.

Answer 1

No.
We know that HCF of the given two numbers must exactly divide their LCM.
But 16 does not divide 380 exactly.
Hence, there can be no two numbers with 16 as their HCF and 380 as their LCM.