a) HCF 25a^2b^{19} & LCM 175a^{25}b^{28}c^{30}

b) HCF 25a^3b^{17} & LCM 375a^{25}b^{28}c^{30}

c) HCF 100a^2b^{28} & LCM 375a^{19}b^{28}c^{30}

d) HCF 25a^3b^{19} & LCM 75a^{5}b^{28}c^{3}

correct answer is: b) HCF 25a^3b^{17} & LCM 375a^{25}b^{28}c^{30}

Explanation

We know,
HCF = Highest Common Factor.
LCM = Least Common Multiple.
Now, the given monomials 25a^3b^{17},75a^{25}b^{19}c^{18} and 125a^{19}b^{28}c^{30} can be factorised as follows:
25a^3b^{17}=5^2\times a^3\times b^{17}
75a^{25}b^{19}c^{18}=3\times5^2\times a^{25}\times b^{19}\times c^{18}
125a^{19}b^{28}c^{30}=5^3\times a^{19}\times b^{28}\times c^{30}
We know that HCF is the highest common factor, so the HCF of 25a^3b^{17},75a^{25}b^{19}c^{18} and 125a^{19}b^{28}c^{30} is:
HCF =5^2\times a^3\times b^{17}=25a^3b^{17}
Also, the LCM is the least common multiple, so the LCM of 25a^3b^{17},75a^{25}b^{19}c^{18} and 125a^{19}b^{28}c^{30} is:
LCM =3\times5^3\times a^{25}\times b^{28}\times c^{30}=375a^{25}b^{28}c^{30}
Ans: HCF is 25a^3b^{17} and LCM is 375a^{25}b^{28}c^{30}