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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 - H.C.F of 4 x 27 x 3125, 8 x 9 x 25 x 7 & 16 x 81 x 5 x 11 49 is?

Answer : C

Explanation

4 x 27 x 3125 = 2² x 3³ x 5⁵; 8 x 9 x 25 x 7 = 2³ x 3² x 5² x 7;
16 x 81 x 5 x 11 x 49 = 2⁴ x 3⁴ x 5 x 7² x 11.
Therefore H.C.F = 180.

Q 2 - Which of the following fractions is the largest?

Answer : A

Explanation

L.C.M of 8, 16, 40 and 80 = 80
⁷⁄₈ = ⁷⁰⁄₈₀; ¹³⁄₁₆ = ⁶⁵⁄₈₀; ³¹⁄₄₀ = ⁶²⁄₈₀
Since ⁷⁰⁄₈₀ > ⁶³⁄₈₀ > ⁶⁵⁄₈₀ > ⁶²⁄₈₀
⁷⁄₈ > ⁶³⁄₈₀ > ¹³⁄₁₆ > ³¹⁄₄₀
S0, ⁷⁄₈ is the largest.

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 two numbers is 48. The numbers are in the ratio 2:3. The sum of the number is?

Answer : A

Explanation

Let the numbers be 2z, and 3z. then their L.C.M = 6z 
 So, 6z = 48 or z = 8.
Therefore the numbers are 16 and 24
Hence the required sum = 40.

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 - H.C.F. of two numbers is 12 and their L.C.M is 72. If the difference between the numbers is 24, their sum is

Answer : C

Explanation

Let the numbers be X & Y
HCF*LCM=Product of two numbers =XY=12x72=864
XY=864 -------- (1)
Given X-Y=24   -------- (2)
On solving 1 & 2 we get X=12 Y=36
Their sum = 12+36=48

Q 8 - The ratio of two numbers is 2:3. Having their L.C.M as 150, numbers are :

Answer : C

Explanation

Let the numbers be  2x and 3x . Then, their L.C.M is 6x.
6x =  150    ⇒ x=  25
So, the numbers are 50 and 75.

Q 9 - Numbers which have 16 as their H.C.F and 136 as their L.C.M , we can definitely say that:

A - only one such pair exists

B - only two such pairs exist.

C - many such pairs exist

D - no such a pair exists

Answer : D

Explanation

H.C.F is always a factor of L.C.M
Since 16 does not divide 136 , so, no such pair exists.

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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