1. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
SHOW ANSWER
Correct Ans:40
Explanation:
Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 48 or x = 8.
The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40.
2. Which of the following has the most number of divisors ?
SHOW ANSWER
Correct Ans:176
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, divisors of 99 are 1, 3, 9, 11, 33, .
99 Divisors of 101 are 1 and 101
Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176
Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
Hence, 176 has the most number of divisors.
3. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
SHOW ANSWER
Correct Ans:127
Explanation:
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127.
4. The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
SHOW ANSWER
Correct Ans:548
Explanation:
Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548.
5. Find the highest common factor of 36 and 84.
SHOW ANSWER
Correct Ans:12
Explanation:
36 = 2^2 x 3^ 2
84 = 2^2 x 3 x 7
H.C.F. = 2^2 x 3 = 12.
6. Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
SHOW ANSWER
Correct Ans:85
Explanation:
ince the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F. of 551 and 1073 = 29;
First number = (551/29 ) = 19 ; Third number = (1073 / 29) = 37
Therefore, Required sum = (19 + 29 + 37) = 85.
7. The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
SHOW ANSWER
Correct Ans:1015
Explanation:
Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7
= 1015
8. The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
SHOW ANSWER
Correct Ans:48
Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
9. What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
SHOW ANSWER
Correct Ans:630
Explanation:
L.C.M. of 12, 18, 21 30 2 | 12 - 18 - 21 - 30
----------------------------
= 2 x 3 x 2 x 3 x 7 x 5 = 1260. 3 | 6 - 9 - 21 - 15
----------------------------
Required number = (1260 ÷ 2) | 2 - 3 - 7 - 5
= 630.
10. 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 again at the starting point ?
SHOW ANSWER
Correct Ans:46 minutes and 12 seconds
Explanation:
L.C.M. of 252, 308 and 198 = 2772.
So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.
11. The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
SHOW ANSWER
Correct Ans:1683
Explanation:
L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
12. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
SHOW ANSWER
Correct Ans:23
Explanation:
L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
Number to be added = (60 - 37) = 23.
13. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:-
SHOW ANSWER
Correct Ans:2
Explanation:
Let the two numbers be 13a and 13b respectively.
Then, 13a x 13b = 2028
=>ab = 2028 / (13*13) = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4). Clearly, there are 2 such pairs.
14. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
SHOW ANSWER
Correct Ans:111
Explanation:
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
=> ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Therefore, Greater number = 111.
15. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
SHOW ANSWER
Correct Ans:9600
Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
16. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
SHOW ANSWER
Correct Ans:4
Explanation:
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
17. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
SHOW ANSWER
Correct Ans:16
Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes, they will toll together 30/2 + 1 = 16 times
18. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
SHOW ANSWER
Correct Ans:4
Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
Are you seeking for good platform for practicing LCM and HCF questions in online. This is the right place. The time you spent in Fresherslive will be the most beneficial one for you.
Online Test on LCM and HCF @ Fresherslive
This page provides important questions on LCM and HCF along with correct answers and clear explanation, which will be very useful for various Interviews, Competitive examinations and Entrance tests. Here, Most of the LCM and HCF questions are framed with Latest concepts, so that you may get updated through these LCM and HCF Online tests. LCM and HCF Online Test questions are granted from basic level to complex level.
Why To Practice LCM and HCF Test questions Online @ Fresherslive?
LCM and HCF questions are delivered with accurate answer. For solving each and every question, very lucid explanations are provided with diagrams wherever necessary.
Practice in advance of similar questions on LCM and HCF may improve your performance in the real Exams and Interview.
Time Management for answering the LCM and HCF questions quickly is foremost important for success in Competitive Exams and Placement Interviews.
Through Fresherslive LCM and HCF questions and answers, you can acquire all the essential idea to solve any difficult questions on LCM and HCF in short time and also in short cut method.
Winners are those who can use the simplest method for solving a question. So that they have enough time for solving all the questions in examination, correctly without any tense. Fresherslive provides most simplest methods to answer any tough questions. Practise through Fresherslive test series to ensure success in all competitive exams, entrance exams and placement tests.
Why Fresherslive For LCM and HCF Online Test Preparation?
Most of the job seekers finding it hard to clear LCM and HCF test or get stuck on any particular question, our LCM and HCF test sections will help you to success in Exams as well as Interviews. To acquire clear understanding of LCM and HCF, exercise these advanced LCM and HCF questions with answers.
You're Welcome to use the Fresherslive Online Test at any time you want. Start your beginning, of anything you want by using our sample LCM and HCF Online Test and create yourself a successful one. Fresherslive provides you a new opportunity to improve yourself. Take it and make use of it to the fullest. GOODLUCK for Your Bright Future.