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.)

Find HCF by using prime factor method:
$54, 81$ and $99$.

  1. $8$
  2. $9$
  3. $10$
  4. $11$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Factorization of the following.
$54 = 2 \times 3 \times 3 \times 3$
$81 = 3 \times 3 \times 3 \times 3$
$99 = 3 \times 3 \times 11$
Since, the common factor is $3 \times 3$,this implies that
$H.C.F = 3 \times 3$
Hence,the correct option $B$.

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

Find $HCF$ by finding factors:
$75, 79$ and $89$.

  1. $2$
  2. $3$
  3. $1$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Factorization of the following 
$75 = 5 \times 5 \times 3\times 1$
$79=1 \times 79$
$89 = 1 \times 89$
Since, the common factor is $1$ this implies that
$HCF = 1$

Hence, the correct option is $C$

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

Find HCF by using prime factor method:
$66$ and $88$.

  1. $21$
  2. $23$
  3. $24$
  4. $22$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Factorization of the following

$66 = 1 \times 3 \times 2 \times 11$
$88 = 1 \times 2 \times 2 \times 2 \times 11$
Since, the common factor is $1,2,11$ this implies that 
$HCF=22$
Hince, the correct option $D$

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

Find HCF by using prime factor method:
$25$ and $55$.

  1. $5$
  2. $3$
  3. $2$
  4. $4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Factorization of the following

$25 = 1 \times 5 \times 5$
$55 = 1 \times 5 \times 11$
Since. the common factor is $1,5$ this implies that 
$HCF=5$
Hence, the correct option $A$

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

What is the HCF of $13$ and $22$?

  1. $13$
  2. $22$
  3. $1$
  4. $286$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Factorization of the following.
HCF=Highest common factor
 so  HCF between $\left( {13,22} \right)$
$ \Rightarrow 13 = 1,13\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - eq.\left( 1 \right)$
$ \Rightarrow 22 = 1,2,11,22\,\,\,\,\,\,\,\,\,\,\, - eq.\left( 2 \right)$  
$(1)$ &$(2)$ equation common is $1$.
Since, The common factor is $1$. This implies that
 then HCF  is $1$.
Hence, the correct option is $C$.
Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

If the HCF of 85 and 153 is expressible in the form 85n $-$ 153, then value of n is :

  1. 3

  2. 2

  3. 4

  4. 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

HCF of $85\  and\  153 = 17$

Now given HCf can be expressed in the gorm of $85n-153$
So $17=85n-173$
On solving the above equation we get $n=2$
So correct answer will be option B

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

Choose the correct answer form the alternatives given.
What is the HCF of $(x^4 \, - \, x^2 \, - \, 6) \, and \, (x^4 \, - \, 4x^2 \, + \, 3)$? 

  1. $x^2$ - $3$
  2. $x + 2$
  3. $x + 3$
  4. $x^2$ + $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle (x^4 \, - \, x^2 \, - \, 6) \, = \, (x^2 \, - \, 3) (x^2 \, + \, 2)$
$\displaystyle (x^4 \, - \, 4x^2 \, + \, 3) \, = \, (x^2 \, - \, 3) (x^2 \, - \, 1)$
HCF is = $x^2$ - $3$

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

The HCF of $2{x^2}$ and $12{x^2}$ is

  1. $2{x^2}$
  2. $12{x^2}$
  3. $2x$
  4. $12x$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$2x^2=2\times x\times x$


$12x^2=6\times 2\times x\times x$

          $=3\times 2\times 2 \times x\times x$

Common factor between $2x^2$ and $12x^2=2\times x\times x=2x^2$

$\therefore$  H.C.F of $2x^2$ and $12x^2$ is $2x^2$.

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

The GCD of two numbers is $17$ and their LCM is $765$. How many pairs of values can the numbers assume?

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

Since the GOD of numbers is $17$. So, the numbers are $17a$ and $17b$, where a and b are relatively prime.
LCM$=765$

$\Rightarrow 17a\times 17b=765$
$\Rightarrow ab=45$
$\Rightarrow a=15, b=9$ or $a=9$, $b=5$.
So, the numbers are $17\times 5=85$ and $17\times 9=153$.
The numbers can be $17\times 1=17$ and $765$. So, two pairs are possible.

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

If two positive integers $a$ and $b$ are written as $a=x^3y^2$ and $b=xy^3$; $x, y$ are prime numbers, then HCF of $a$ and $b$ is

  1. $xy$
  2. $xy^2$
  3. $x^3y^3$
  4. $x^2y^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given,

$a={  x}^{3  }{ y }^{2  } = x\times x\times x\times y\times y$

$b={  x}{ y }^{3  }         =x\times y\times y\times y$

H.C.F of $a,b$  = ${  x}{ y }^{2  } $

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

If HCF of $m$ and $n$ is $1,$ then what are the HCF of $m + n, m$ and HCF of $m - n, n$ respectively? 

$\displaystyle \left ( m> n \right )$

  1. $1$ and $2$
  2. $2$ and $1$
  3. $1$ and $1$

  4. cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let us consider an example.
Let $m =16$ and $n =9$ be relatively prime numbers.
So, $m+n=25$. The HCF of $25$ and $16$ is $1$. 

$m-n=7$. The HCF of $7$ and $9$ is $1$.
Similarly, if we take other values for $m$ and $n,$ we get the same answer. 
Therefore, option $C$ is correct.