Question

Find HCF AND LCM of 60,84 and 108 by prime factorization method

Answer 1

60 = 2*30

=2*2*15

=2*2*3*5

84 = 2*42

=2*2*21

=2*2*7*3

108 = 2*54

=2*2*27

=2*2*3*9

=2*2*3*3*3

Hence,

LCM = 2*2*3*3*3*7*5

=4*27*5

=540

HCF = 2*2*3

=12

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\bold{\begin{array}{r | 1} 2 & 60 \\ \cline{2-2} 2 & 30 \\ \cline{2-2} 3 & 15 \\ \cline{2-2} & 5 \end{array}}$

$\begin{array}{r | 1} 2 & 84 \\ \cline{2-2} 2 & 42 \\ \cline{2-2} 3 & 21 \\ \cline{2-2} & 7 \end{array}$

$\begin{array}{r | 1} 2 & 108 \\ \cline{2-2} 2 & 54 \\ \cline{2-2} 3 & 27 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} & 3 \end{array}$

Now :-

60 = (2² × 3 × 5)

84 = (2² × 3 × 7)

108 = (2² × 3³)

★LCM = 2 × 2 × 3 × 3 × 3 × 7 × 5

= 4 × 27 × 5

= 540

★HCF(60,84,108) = (2² × 3) = 12

$\Large{\boxed{\sf\:{Additional\; Information}}}$

In case :-

★Three positive integers a,b,c

★HCF(a,b,c) × LCM(a,b,c) ≠ a × b × c

$\tt{\rightarrow LCM(a,b,c)\dfrac{a\times b\times c\times HCF (a,b,c)}{HCF(a,b)\times HCF(b,c)\times HCF(a,c)}}$

$\tt{\rightarrow HCF(a,b,c)\dfrac{a\times b\times c\times LCM (a,b,c)}{LCM(a,b)\times LCM(b,c)\times LCM(a,c)}}$