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H.C.F and L.C.M Questions

Home > Quantitative Aptitude > H.C.F and L.C.M > General Questions
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The ratio of two numbers is 3:4 and their HCF is 4.Their LCM is:


A12

B16

C24

D48

Answer: Option D

Explanation:

Given Two No, ratio = 3:4 and their HCF = 4
So, No. = 3*4 =12 and 4*4=16
LCM of 12,16 = 48

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find the number between 100 to 400 which is divisible by either 2,3,5,7..


A120

B100

C205

D210

Answer: Option D

Explanation:

LCM of 2,3,5,7=210

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A teacher can divide her class into groups into groups of 5,13 and 17. What is the smallest possible strength of the class?


A835

B940

C1105

D1220

Answer: Option C

Explanation:

For smallest possible class strength, we consider LCM of the given numbers. So LCM (5, 13, 17) = 1105.

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If an integer k is divisible by 2,5 and 13, what is the next largest number that is divisible by all the three given numbers ?


Ak+130

Bk+13

C2k+13

D2k+65

E2k

Answer: Option A

Explanation:

k+ LCM of 2,5,13
=> (k + 130)

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What is the least amount that a person can have, such that when he distributes it into groups of Rs.16 or Rs. 18 or Rs. 20 or Rs. 25, he is always left with Rs. 4?


ARs. 1796

BRs. 1804

CRs. 2596

DRs. 3604

Answer: Option D

Explanation:

Find the lcm of 16 18 20 and 25 i.e 3600.
so the amount is (3600 + 4) = Rs. 3604

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HCF of 2472,1284 and a third number 'n'is 12.If their LCM is 8*9*5*103*107.then the number 'n'is..


A2^2*3^2*5^1

B2^2*3^2*7^1

C2^2*3^2*8103

DNone of these

Answer: Option A

Explanation:

2472 = 2^3×3×103
1284 = 2^2×3×107
HCF = 2^2×3
LCM = 2^3×3^2×5×103×107
HCF of the numbers is the highest number which divides all the numbers. So N should be a multiple of 2^2×3
LCM is the largest number that is divided by the given numbers. As LCM contains 32×5 these two are from N.
So N = 2^2×3^2×5^1

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In a circular racetrack of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite at 15 m/s. When will all the three meet for the first time after the start?


A100

B120

C110

D150

Answer: Option A

Explanation:

Since the track is a circular track A and B will meet every 50 seconds. i.e. 100 / (10-8).
Since it is a multiple of 50 they will be meeting at the starting point every 50 Seconds.
If you multiply 15 x 50 you will get 750 and after the second 50 it will be 1500.
All of them will meet at the starting point after 100

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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:


A1677

B1683

C1898

D3363

ENone of these

Answer: Option B

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 * 2 + 3) = 1683.

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At a stadium a certain rows are to be reserved to accommodate 12 cricket players 24 football players and 32 soccer players. How many minimum rows need to be reserved if same number of players of only one category are to be seated in each rows


A8

B34

C17

D4

ENone of these

Answer: Option D

Explanation:

Solution: Basically they are asking for the H.C.F of 12, 24 and 32 to find out the H.C.F of them



The answer is 4 WHICH IS THE MINIMUM number of rows required.

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What is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder?


A257

B905

C351

D498

Answer: Option A

Explanation:

Given numbers are 90207,127986 and 232585.

To Get the greatest number which divides given numbers without leaving a remainder.

i.e find the HCF of given numbers.
90207=3*3*3*13*257
127986=2*3*83*257
232585=5*181*257
=> 257 is the largest number.

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