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H.C.F & L.C.M. - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to H.C.F & L.C.M.. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Q 1 - Find L.C.M and H.C.F of 0.63, 1.05 and 2.1.

A - H.C.F 0.26 and L.C.M 6.35

B - H.C.F 0.25 and L.C.M 6.00

C - H.C.F 0.23 and L.C.M 7.30

D - H.C.F 0.21 and L.C.M 6.30

Answer : D

Explanation

Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10.
without decimal places, these numbers are 63, 105, and 210
Now, H.C.F of 63, 105 and 210 is 21 so H.C.F of 0.63, 1.05 and 2.1 is 0.21 
 L.C.M of 63, 105 and 210 is 630 so L.C.M of 0.63, 1.05 and 2.1 is 6.30

Q 2 - The greatest number of four digits which is exactly divisible by 15, 25, 40, and 75 is?

Answer : C

Explanation

Greatest number of 4 digits is 9999. L.C.M  of 15, 25, 400 and 75 is 600. 
 On dividing 9999 by 600, the remainder  is 399. 
 Required number = (9999 - 399) = 9600.

Q 3 - A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?

A - 42 minutes 36 seconds

B - 26 minutes 18 seconds

C - 45 minutes

D - 46 minutes 12 seconds

Answer : D

Explanation

L.C.M of 252, 308 and 198 = 2772, 
 So A,B,C will again meet at the starting point in 2772 sec. i.e 46 minutes 12 seconds

Q 4 - Product of the two co-prime numbers is 117. Their L.C.M should be?

Answer : D

Explanation

H.C.F of Co-prime number is 1. So, L.C.M = ¹¹⁷⁄₁ = 117

Q 5 - L.C.M of two prime numbers a and b(a>b) is 161. The value of 3b - a is?

Answer : B

Explanation

H.C.F of two prime numbers is 1. Product of numbers = (1 x 161) = 161
Let the numbers be a and b. Then a x b = 161
now co-primes with product 161 are (1, 161) (7,23).
Since a and b are prime numbers and a > b, we have a = 23 and b = 7.
Therefore  3b - a = (3 x 7) - 23 = -2.

Q 6 - Find the least number which when divided separately by 13, 26, 39 and 52 leaves 5 as remainder in each case.

Answer : C

Explanation

Required number = L.C.M. of (13, 26,39 and 52) +5
= 156 + 5 = 161

Q 7 - If the sum of two numbers is 175 and the H.C.F. and L.C.M. of these numbers are 35 and 140 respectively, then the sum of the reciprocals of the numbers is equal to:

Answer : A

Explanation

Let the numbers be X and Y.
Then, X+Y = 175 and XY = 35x140 = 4900.
The required sum =  1/X+1/Y=(X+Y)/XY=175/4900 = 1/28

Q 8 - Sum of two numbers is 60 and their H.C.F and L.C.M are 12 and 72 respectively. One of the numbers is:

Answer : B

Explanation

Let the numbers be  12 a and 12 b, where a and b are co primes.
Then, 12 a *12 b = 12 *72  ⇒ ab= 6
co-primes with product 6 are a = 2, b= 3
∴ numbers are (12*2, 12*3 ) i.e  24 and 36

Q 9 - The ratio of two numbers is 15:11. Having their H.C.F as 13 ,numbers are:

Answer : D

Explanation

Let the numbers be 15x  and 11x . Then , their H.C.F is x.
∴ x= 13 and so the numbers are (15*13, 11*13) i.e , 195, 143

Q 10 - If the capacity of two pots is 120 liters and 56 liters. Find the container capacity which can exactly measure the contents of the two pots, is :

Answer : C

Explanation

Required capacity = H.C.F of 120 L and 56 L.= 8 L = 8000cc

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