Question

What is the L.C.M. of 10/21, 20/63, 55/56?

Answer 1

Step-by-step explanation:

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Answer 2

$\displaystyle \sf{ LCM \: of \: \: \frac{10}{21} \: , \: \frac{20}{63} \:, \: \frac{55}{56} } = \frac{220}{7}$

Given :

$\displaystyle \sf{ \frac{10}{21} \: , \: \frac{20}{63} \:, \: \frac{55}{56} }$

To find :

$\displaystyle \sf{ LCM \: of \: \: \frac{10}{21} \: , \: \frac{20}{63} \:, \: \frac{55}{56} }$

Solution :

Step 1 of 3 :

Find LCM of 10 , 20 , 55

We first prime factorise the given numbers

10 = 2 × 5

20 = 2 × 2 × 5

55 = 5 × 11

LCM of 10 , 20 , 55

= 2 × 2 × 5 × 11

= 220

Step 2 of 3 :

Find HCF of 21 , 63 , 56

We first prime factorise the given numbers

21 = 3 × 7

63 = 3 × 3 × 7

56 = 2 × 2 × 2 × 7

HCF of 21 , 63 , 56 = 7

Step 3 of 3 :

Find the required LCM

$\displaystyle \sf{ LCM \: of \: \: \frac{10}{21} \: , \: \frac{20}{63} \:, \: \frac{55}{56} }$

$\displaystyle \sf{ = \frac{LCM \: of \: \: 10 , 20 , 55}{HCF \: of \: \: 21 , 63 , 56} }$

$\displaystyle \sf{ = \frac{220}{7} }$