Olympiad Test : Playing With Numbers - 1 - Class 6 MCQ

HCF × LCM = product of numbers.

2 + 4 + 3 + 5 + 7 + 8 + 0 + 6 = 35
3 + 3 + 3 + 3 + 6  + 4 + 3 + 3 = 28
3 + 5 + 7 + 6 + 9 + 8 + 1 + 2 = 41 
8 + 3 + 4 + 7 + 9 + 5 + 6 + 0 = 42
Since 42 is divisible by 3 then (d) is divisible by 3. 

117, 171 are divisible by 3.
169 is divisible by 13.
179 is a prime number.

(23, 31) is not a twin prime. 
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (17, 19) or (41, 43).

HCF of 120 and 144 = 12
HCF of 120 and 204 = 12
Required number = HCF of 120, 144, 204 = 12

HCF of 72 and 108 = 36
HCF of 108 and 180 = 36
∴ required number = 36 

LCM of 16, 36 and 40 is

∴ LCM = 2 × 2 × 2 × 2 × 9 × 5
= 16 × 45 = 720
∴ required number = (720+7) = 727

The greatest 4 digit number = 9999. Here,

LCM of 12, 16, 28 and 36
= 2 × 2 × 2 × 3 × 2 × 7 × 3 
= 4 × 9 × 4 × 7 
= 16 × 9 × 7 
= 1008
∴ 9072 is a multiple of 1008.
∴  it is the greatest number of 4 digits which is divisible by 12, 16, 28 & 36.

LCM × HCF = one number × second number

LCM of 21, 28, 36 and 45 is

∴ LCM of 21, 28, 36 and 45
= 3 × 2 × 3 × 2 × 7 × 5
= 36 × 35 
= 1260
∴ Required number = 1260 + 3 = 1263