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

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 the lowest common multiple of 24, 36 and 40?

Answer : B

Explanation

L.C.M = 2 x 2 x 2 x 3 x 3 x 5 = 360

Q 2 - The ratio of two numbers is 3:4 and their H.C.F is 4. Their L.C.M is?

Answer : C

Explanation

Let the numbers be 3x and 4x.
Then, their H.C.F = z
So, z = 4 
 So, the numbers are 12 and 16. L.C.M of 12 and 16 = 48.

Q 3 - Let the least number of six digit, which when divided by 4,6,10 and 15, leaves in each case the same remainder of 2. The sum of the digits N is?

Answer : A

Explanation

Least number of 6 digits  is 100000. L.C.M of 4,6,10 and15 = 60
On dividing 100000 by 60, the remainder obtained is 40.
Therefore Least number of 6 digits divisible by 4,6,10, and 15 = 100000 + (60 - 40) = 100020.
Therefore N = (100020 + 2) = 100022.
Sum of digits in N = (1 + 2 + 2) = 5.

Q 4 - The L.C.M of the two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10 then their difference is?

Answer : D

Explanation

Let the numbers be z and (100 - z). Then, z (100 - z) = 5 x 495
= z² - 100z + 2475 = 0
(z - 55) (z - 45) = 0
z = 55 or z = 45 
 Therefore the numbers are 45 and 55. Required difference is (55 - 45) = 10

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 - The number of prime factors in the expression 2⁵x2⁶x3⁶x5³

Answer : A

Explanation

2, 3, 5 are the prime numbers and the given expression is 2⁵x2⁶x3⁶x5³ (2⁵x6⁶x5³).
So the total would be the sum of powers in the expression that is 5+6+6+3=20

Q 7 - The G.C.D. of 0.93, 0.60 and 0.75 is:

Answer : A

Explanation

Given numbers are 0.93, 0.60 and 0.75.   H.C.F. of 93, 60 & 75 is 3.
 H.C.F. of given numbers = 0.03

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 - If the H.C.F of two numbers is 8. Then following number cannot be the L.C.M of these numbers.

Answer : D

Explanation

The H.C.F of two numbers always divides their L.C.M.
Since 8 does not divide 60, so, 60 cannot be their L.C.M.

Q 10 - Find the largest fraction among the following:

Answer : A

Explanation

L.C.M of 8, 16,40 , 80 is 80.
7/8  =  (7/8 *10/10 ) = 70/80  , 13/16 = (13/16*5/5)=  65/80 ,31/40 = (31/40* 2/2 )= 62/80,63/80
Clearly ,70/80 > 65/80 >63/80 >62/80 . Hence, 7/8 is the largest.

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