Question

Find HCF and LCM of 60 , 84 and 108 using F.T.A

Answer 1

Answer:

12 & 3780

Step-by-step explanation:

Prime factors:

60= 2*2*3*5

84= 2*2*3*7

108 = 2*2*3*3*3

HCF(60,84,108) = 2*2*3= 12

LCM(60,84,108) = 2*2*3*3*3*5*7 = 3780

Answer 2

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➝ Prime factorisation of 60,84 and 108 :-

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

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

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

Now,

we have,

• 60 = (2 × 2 × 3 × 5) = ( 2² × 3 × 5)

• 84 = (2 × 2 × 3 × 7) = (2² × 3 × 7)

• 108 = (2 × 2 × 3 × 3 × 3) = (2² × 3³)

So,

HCF (60,84,108) = (2² × 3) = (4 × 3) = 12

LCM (60,84,108) = (2² × 3³ × 5 × 7) =( 4 × 27 × 5 × 7) = 3780

Hence,the HCF and LCM of (60,84,108) will be 12 and 3780.

More information,

When we find HCF and LCM of given number by using prime factorisation then,

HCF (given number) = product of the smallest power of each common prime factors in the numbers.

LCM (given number) = product of the greatest power of each prime factors involved in the numbers.