Question

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 $25$
(iv) $40,36$ and $126$ (v) $84,90$ and $120$ (vi) $24,15$ and $36$

Answer 1

$1)12=2^2\times 3,15=3\times 5,21=3\times 7$

$⟹LCM=2^2\times 3\times 5\times 7=420,HCF=3$

$2)17={17}^1,23={23}^1,{29}^1$

$⟹LCM=17\times 23\times 29=11339,HCF=1$

$3)8=2^3,9=3^2,25=5^2$

$⟹LCM=2^3\times 3^2\times 5^2=1800,HCF=1$

$4)40=2^3\times 5,36=2^2\times 3^2,126=2\times 3^2\times 7$

$⟹LCM=2^3\times 3^2\times 5\times 7=2520,HCF=2$

$5)84=2^2\times 3\times 7,90=2\times 3^2\times 5,120=2^3\times 3\times 5$

$⟹LCM=2^3\times 3^2\times 5\times 7=2520,HCF=2\times 3=6$

$6)24=2^3\times 3,15=3\times 5,36=2^2\times 3^2$

$⟹LCM=2^3\times 3^2\times 5=360,HCF=3$