The L.C.M of  22, 54, 108, 135 and 198 is

 

From the given data,

containers contain mixtures of milk and water as 1365 lit, 1560 lit and 1755 lit.

Biggest measure that can measure all these different quantities exactly can be given by

HCF of (1365, 1560, 1755) 

That can be found as 

HCF of 1365, 1755 = 195

Now, HCF of 195 and 1560 = 195

Hence, biggest measure that can measure all the given different quantities exactly is 195 lit.

If the Multiples for two or more numbers which are Common, then those Multiples are said to be Common Multiples. 

For Example :

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...

Multiples of 5 are 5, 10, 15, 20, 25, 30,...

Here common multiples of 3 & 5 upto 30 are 15, 30.

  LCD is nothing but Lowest or Least Common Denominator

Here LCD of 12 and 18 means LCD of two fractions with denominators 12 and 18 respectively.

Therefore, LCM of 12 & 18 = 6 x 3 x 2 = 36 

•  How to calculate LCD ::

The lowest common denominator or least common denominator (LCD) is the least common multiple (LCM) of the denominators of a set of fractions.

Here the LCM of 54, 60 is

=> 2 x 3 x 3 x 3 x 10

= 6 x 9 x 10

= 54 x 10

= 540.

HCF of 210 and 55 is 5

Now, 210x5 + 55P = 5

=> 1050 + 55P = 5

=> 55P = -1045

=> P = -1045/55

=> P = -19.

To get the least number of coconuts :
LCM = 30 => 30 + 1 = 31

The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.
Number of cans of Maaza = 368/16 = 23
Number of cans of Pepsi = 80/16 = 5
Number of cans of Sprite = 144/16 = 9
The total number of cans required = 23 + 5 + 9 = 37 cans.

4 x 27 x 3125 = 22 × 33 × 55 ;

8 x 9 x 25 x 7 = 23 × 32 × 52 × 7

16 x 81 x 5 x 11 x 49 = 24 × 34 × 5 × 11 × 72

H.C.F = 22 × 32 × 5 = 180.