Question

Find the $LCM$ and $HCF$ of given pair numbers by prime factorisation method
(i) $120,90$
(ii) $60,60$
(iii) $37,49$

Answer 1

HCF of numbers = product of the smallest power of each common - prime factors of the number

LCM of number= product of greatest power of each prime factors of the number

(1) 120, 90

$120\Rightarrow 2\times 2\times 2\times 3\times 5=2^3\times 3\times 5$

$90\Rightarrow 2\times 3\times 3\times 5=2\times 3^2\times 5$

$HCP\Rightarrow 2\times 3\times 5=30$

$L.CM\Rightarrow 2^3\times 3^2\times 5=360$

(2) 50,60

$50\Rightarrow 2\times 5\times 5$

$=2\times 5^2$

$60=2\times 2\times 3\times 5=2^2\times 3\times 5$

$HCF=2\times 5=10$

$LCM=2^2\times 3\times 5^2=300$

(3) 37,49

$37\times 1=37$

$49\Rightarrow 7^2$ HCF = 1

LCM = $37\times 7^2=1086$