Given
No. of the floors = 108
Two lifts A and B starting from the ground floor, stop at every 3rd and 5th floors respectively.
= 3 \(\times\) 5 = 15
Therefore The lifts will stop at floors 15, 30, 45, 60, 75, 90 and 105.

Given: numbers are 1 to 9.

Therefore the smallest number
= \(2 \times 2 \times 3 \times 3 \times 5 \times 7 \times 2\)
= 2520

All the prime numbers between 10 and 20 are 11, 13, 17 and 19
sum = 11 + 13 + 17 + 19
= 60 - single digits ( 1 to 9 )
i)  60 is divisible by 1.
ii)  60 is divisible by 2.
iii)  60 is divisible by 3.
iv)  60 is divisible by 4.
v)  60 is divisible by 5.
vi)  60 is divisible by 6.
vii)  60 is not divisible by 7, 8 and 9.
Therefore the sum 60 is divisible by 1, 2, 3, 4,  5 and 6.

Given: 40 seconds, 60 seconds and 72 seconds

LCM = \(2 \times 2 \times 5 \times 2 \times 3 \times 3\) = 360 seconds
Also given, they changed simultaneously together at 8 a.m.
Therefore 360 seconds = 6 min
⇒ 1 hour = 60 min
Therefore 8 a.m. + 6 min = 8.00 + 0.06
Time = 8.06 a.m.
After 360 seconds, therefore 8.06 a.m. will they simultaneously change together again.

Given: 80 litres, 100 litres and 120 litres.
Greatest possible volume of a vessel.

Therefore HCF = 5 \(\times\) 2 \(\times\) 2 = 20
Therefore the greatest possible volume of a vessel = 20 l milk.

i) LCM

Therefore LCM = \(2 \times 11 \times 7 \times 9 \times 13\) = 18018
ii) HCF

Therefore HCF = 2 \(\times\) 11 = 22

The given prime number 13 can be reversed
to get another prime number 31.
Similarly, other any such pairs are (17, 71), (37, 73) and (79, 97)

Let 3 odd natural numbers are 3, 7 and 9.
Sum = 3 + 7 + 9 = 19 is odd.
This statement is true.

The smallest 3 digit composite number = 100
The biggest three digit composite number = 999

The Smallest two digit prime number = 11
The Biggest two digit prime number = 97