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

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)

Multiple choice

Find the HCF of 24 and 32

  1. 96

  2. 56

  3. 8

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

[Explanation: Factors of 24 are 1,2,3,4,6,8,12,24 Factors of 32 are 1,2,4,8,16,32 Common factors of 24 and 32 are 1,2,4,8 Highest common factor(HCF)= 8]

Multiple choice

Find the HCF and LCM of 25, 65

  1. 5, 325

  2. 1,90

  3. 325, 5

  4. 90,1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

[Explanation: Prime factors of 25= 5 x 5 Prime factors of 65= 13 x 5 LCM of 25 and 65= 5 x 5 x 13= 325 Now, HCF= Product of numbers/LCM= (25 x 65)/325= 5]