Quantitative Aptitude · Mathematics

HCF and LCM

233 Questions

Improve your quantitative aptitude speed by solving these HCF and LCM questions. The problems involve finding the highest common factor and least common multiple for sets of numbers. These calculations form a core part of the mathematics section in SSC, banking, and railway recruitment exams.

Finding HCFFinding LCMGreatest common factorLeast common multipleNumber properties

HCF and LCM Questions

Multiple choice

Four bells toll together at 9.00 am. They toll after 7, 8, 11 and 12 seconds, respectively. How many times will they toll together again in the next 3 hours?

  1. 3

  2. 4

  3. 5

  4. 9

  5. 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The LCM of 7, 8, 11 and 12 is 1848. So, the bells will toll together after every 1848 seconds. In 1848 seconds, all four bells toll 1 time. In 3 hrs (3 x 60 x 60), i.e. 10800 seconds, they will toll 3 x 60 x 60/1848 times = 5.84 times. As it has to be an integral part, so the answer is 5.

Multiple choice

The HCF of 2472, 1284 and a third number N is 12. If their LCM is 23 x 32 x 5 x 103 x 107, then the number N is

  1. 22 x 32 x 7

  2. 22 x 33 x 103

  3. 22 x 32 x 5

  4. 24 x 32 x 11

  5. 21 x 33 x 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

2472 = 2 x 2 x 2 x 3 x 103 1284 = 2 x 2 x 3 x 107 N = 2 x 2 x 3 x y (2, 2, 3 are common values and should product with y) HCF = 2 x 2 x 3 = 12 LCM = 2 x 2 x 3 x y x 2 x 103 x 107 We know the LCM and solve to find y. We get 15 Now, N = 180 = 22 x 32 x 15

Multiple choice

Three colours of chart papers: green, red and blue have to arranged in such a way that all the chart papers are stored colourwise and height of each bundle is the same. The number of green chart papers is 96, of red chart papers is 240 and of blue chart papers is 336. Thickness of each chart paper is the same. Determine the number of bundles of green, red and blue, respectively.

  1. 35, 14, 10

  2. 48, 48, 48

  3. 2, 5, 7

  4. 32, 80, 112
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In order to arrange chart papers as required we have to find
 
the largest number that divides 96,240 and 336.Clearly such
number is their H.C. F.
96  = 2 x 2 x 2 x 2 x 2 x 3
 
240 = 2 x 2 x 2 x 2 x 3 x 5
 
336 = 2 x 2 x 2 x 2 x 3 x 7
 
H.C.F. = 2 x 2 x 2 x 2 x 3 = 48
 
 
Hence there must be 48 chart papers in each bundle
 
 Number of green chart paper bundles = 96/48 = 2

Number of red chart paper bundles = 240/48 = 5 Number of blue chart paper bundles = 336/48 = 7

 

Multiple choice

LCM of 2/5, 3/10 and 6/25 is

  1. 1/5

  2. 6/5

  3. 2/5

  4. 12/25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

LCM of numerators divided by GCD of denominators:  LCM of numerators is 6. HCF of denominators is 5. So, the LCM of given terms is 6/5.

Multiple choice

The LCM of (a3 + b3) and (a4 - b4) is

  1. (a3 + b3) (a + b) (a2 + b2)

  2. (a3 + b3) (a2 + b2) (a - b)

  3. (a + b) (a2 + ab + b2)

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

a3 + b3 = (a + b) (a2 - ab + b2) and a4 - b4 = (a - b) (a + b) (a2 + b2)

HCF = a + b Hence, LCM = (a3 + b3) (a - b) (a + b) (a2 + b2) / (a + b) = (a3 + b3) (a - b) (a2 + b2)