Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) $12,15$ and $21$ (ii) $17,23$ and $29$ (iii) $8,9$ and $25$

Using prime factorisation method:

(i) 12, 15 and 21

Factor of $12=2\times 2\times 3$

Factor of $15=3\times 5$

Factor of $21=3\times 7$

HCF $(12,15,21)=3$

LCM $(12,15,21)=2\times 2\times 3\times 5\times 7=420$

(ii) 17, 23 and 29

Factor of $17=1\times 17$

Factor of $23=1\times 23$

Factor of $29=1\times 29$

HCF $(17,23,29)=1$

LCM $(17,23,29)=1\times 17\times 23\times 29=11,339$

(iii) 8, 9 and 25

Factor of $8=2\times 2\times 2\times 1$

Factor of $9=3\times 3\times 1$

Factor of $25=5\times 5\times 1$

HCF $(8,9,25)=1$

LCM $(8,9,25)=2\times 2\times 2\times 3\times 3\times 5\times 5=1,800$