Quantitative Aptitude · Mathematics

HCF and LCM

215 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 maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

HCF of $24 $ and $36$ is ..............

  1. $6$
  2. $4$
  3. $9$
  4. $12$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$2\underline {|24} {\;} 2\underline {|36}$
$2\underline {|12} {\;} 2\underline {|18}$
$2\underline {|6} {\;} 3\underline {|9}$
$3\underline {|3} {\;} 3\underline {|3}$
    1    1
$24 = 2 \times 2 \times 2 \times 3$
$36 = 2 \times 2 \times 3 \times 3$
$\therefore H.C.F=2\times 2 \times 3=12$
Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

HCF of the numbers $36$ and $144$ is 

  1. $36$
  2. $144$
  3. $4$
  4. $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Factors of the given numbers are,

$36= 2\times 2 \times 3 \times 3$
$144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 $
$\therefore $ HCF of $36$ and $144$ $ = 2 \times 2 \times 3 \times 3 = 36$


Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The product of two numbers is $2240$ and their HCF is $14$. Which of the following is not the possible pair.

  1. $(14,160)$
  2. $(28,80)$
  3. $(42, 80)$
  4. $(56,40)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pair in Option C is not possible.
because in option C pair is $(42,80)$
Since, Product of numbers $=42\times 80 =3360$
Option C is correct.

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The HCF of $3^5$, $3^9$, and $3^{14}$ is

  1. $3^5$
  2. $3^9$
  3. $3^{14}$
  4. $3^{28}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

${ 3 }^{ 5 }$ = 3x3x3x3x3

${ 3 }^{ 9 }$ = 3x3x3x3x3x3x3x3x3
${ 3 }^{ 14 }$ = 3x3x3x3x3x3x3x3x3x3x3x3x3x3x3
Common factors are 3x3x3x3x3
SO HCF will be ${ 3 }^{ 5 }$
Correct answer will be option A

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The GCD and LCM of two numbers a and b are, respectively, 27 and 2079. If a is divided by 9, the quotient is 21. Then b is

  1. $243$
  2. $189$
  3. $113$
  4. $297$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the two numbers be $a$ and $b$.
$a=quotient\times dividend$
$a=21\times 9$
  $=189$
$\therefore b=\frac { GCD\times LCM }{ a }$
                  $=\frac { 27\times 2079 }{ 189 }$
                  $=297$

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The H.C.F. of $\dfrac { 9 }{ 10 }$, $\dfrac { 12 }{ 25 }$, $\dfrac { 18 }{ 35 }$ and $\dfrac { 21 }{ 40 } $ is:

  1. $\dfrac { 3 }{ 5 } $
  2. $\dfrac { 252 }{ 5 } $
  3. $\dfrac { 3 }{ 1400 } $
  4. $\dfrac { 63 }{ 700 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Required H.C.F. $=\dfrac { H.C.F.\quad of\quad 9,12,18,21 }{ L.C.M.\quad of\quad 10,25,35,40 } = \dfrac { 3 }{ 1400 } $

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

What is the HCF of $3.0, 1.2$ and $0.06$?

  1. $0.6$
  2. $0.06$
  3. $6.0$
  4. $6.06$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given terms are $\dfrac {3}{1}, \dfrac {6}{5}$ and $\dfrac {3}{50}$.
H.C.F. of these terms $= \dfrac {\text{H.C.F. of}\ 3, 6, 3}{\text{L.C.M. of}\ 1, 5, 50}$
$= \dfrac {3}{50} = 0.06$

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find $HCF$ by finding factors:
$16$ and $56$.

  1. $6$
  2. $18$
  3. $8$
  4. $9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Factorization of the following.
$16 = 2 \times 2 \times 2 \times 2$
$56 = 2 \times 2 \times 2 \times 7$
Since, the common factor is $2,2,8$,this implies that
$H.C.F = 2 \times 2 \times 2$
           $=8$
Hence,the correct option $C$.