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

What is the greatest common factor?

  1. The smallest of the large factors

  2. The largest of the common factors

  3. The sum of the common factors

  4. The first multiple of the largest factor
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The largest of the common factors

Multiple choice

If the greatest common factor (GCF) of two numbers is one of those numbers then their least common multiple(LCM) shall be

  1. The smaller of the two numbers

  2. The product of the two numbers

  3. The larger of the two numbers

  4. The difference of the two numbers

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the Greatest Common Factor (GCF) of two numbers is one of those numbers then their Least Common Multiple(LCM) shall be the larger of the two numbers.

For e.g. if the two numbers are 4 & 8 then HCF or GCF is 4 but LCM shall be 8.

Multiple choice

A rectangular field measures 480 m x 144 m and is to be paved with square tiles. The owner wants the field to be paved with SQUARE tiles with MAXIMUM covering area. Find the size of such a square tile and the total number of tiles equired to completely pave the field.

  1. 96 & 7 respectively

  2. 24 & 120 respectively

  3. 48 & 30 respectively

  4. 36 & 54 respectively

  5. 72 & 7 respectively
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Correct.

The maximum size of square tile shall be equal to the Greatest Common Divisor (GCD) of the length and breadth, i.e. 480, 144, which is 48. 

The total no. of tiles is = 480 x 144/(48 X 48) = 30.

Multiple choice

The LCM of 5, 8, 12 and 20 will not be a multiple of

  1. 5

  2. 3

  3. 9

  4. 20

  5. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

5 = 58 = 2 x 312 = 2 x 2 x 320 = 2 x 2 x 5 LCM = 2 x 3 x 3 x 5 (Take highest power of common factor 2, 5 and remaining left out factor 3) = 120 By definition of LCM, 5, 8, 12 and 20 have to be multiples of 120, so the left out number 9 will not be a multiple of LCM.