Aptitude - Questions & Answers

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 - Which of the following has most number of divisors?

Answer : B

Explanation

99 = 1 x 3 x 3 x 11;
101 = 1 x 101;
176 = 1 x 2 x 2 x 2 x 2 x 11;
182 = 1 x 2 x 7 x 13.
So, divisor of 99 are 1, 3, 9, 11, 33, 99
divisor of 101 are 1, 101
divisor of 176 are 1, 2, 4, 8, 16, 22, 44, 88, 176
divisor of 182 are 1, 7, 2, 13, 14, 26, 91, 182
Hence 176 has the most number of divisors.

Q 2 - H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 2⁴ x 3 ⁵ x 5² x 7²?

A - 2³ x 3 ⁵ x 5² x 7²

B - 2² x 3 ⁵ x 7²

C - 2² x 5 x 7²

D - 2⁵ x 5 ² x 7²

Answer : B

Explanation

3240 = 2³ x 3² x 5; 3600 = 2⁴ x 3² 5²
H.C.F = 36 = 2² x 3².
Since H.C.F is the product of the lowest powers of common factors so the the third number must have 2² x 3² as its factor
Since L.C.M is the product of highest powers of common prime factors so the third number must have 3⁵ x 7² as its factor
Therefore third number = 2² x 3⁵ x 7²

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 - The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is?

Answer : B

Explanation

Other number = ^{11 x 7700}⁄₂₇₅ = 308

Q 5 - A rectangular courtyard 3.78 meters long and 5.25 meters wide is to be paved exactly with square titles all of the same size. What is the largest size of the tile which could be used for the purpose?

A - 21 cms

B - 14 cms

C - 42 cms

D - none of the above.

Answer : A

Explanation

Largest size of the tile = H.C.F of 378 cm and 525 cm = 21 cms.

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 - The L.C.M and H.C.M of two numbers is 2310 and 30. If one of these numbers is 210, what is the second number?

Answer : A

Explanation

Let the second number be x. Then,
2310 * 30  = 210 *x ⇒x = (2310 *30)/210 =  330
∴ the second number is 330.

Q 9 - The H.C.F of three numbers is 12 and they are in the ratio of 1:2:3, find the numbers.

Answer : C

Explanation

Let the numbers be a, 2a , 3a . Then , their H.C.F is a.
∴  a =12  and hence , the numbers  are 12, 24, 36.

Q 10 - If the H.C.F of two numbers is 24 then number which can be their L.C.M is:

Answer : B

Explanation

H.C.F always divides L.C.M completely.
∴ L.C.M  is 120.

aptitude_hcf_lcm.htm

Print Page