# H.C.F and L.C.M Problems Question & Answers

## HCF and LCM Problems

Quantitative aptitude questions are asked in many competitive exams and placement exam.'HCF and LCM' is a category in Quantitative Aptitude. Quantitative aptitude questions given here are extremely useful for all kind of competitive exams like Common Aptitude Test (CAT), MAT, GMAT, IBPS Exam, CSAT, CLAT, Bank Competitive Exams, ICET, UPSC Competitive Exams, CLAT, SSC Competitive Exams, SNAP Test, KPSC, XAT, GRE, Defense Competitive Exams, L.I.C/ G. I.C Competitive Exams, Railway Competitive Exam, TNPSC, University Grants Commission (UGC), Career Aptitude Test (IT Companies) and etc., Government Exams etc.

We have a large database of problems on “H C F and L C M” answered with explanation. These will help students who are preparing for all types of competitive examinations.

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

 A) 123 B) 127 C) 235 D) 305

Explanation:

Required number = H.C.F. of (1657 - 6) and (2037 - 5)

= H.C.F. of 1651 and 2032 = 127.

Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability

36

A rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square  tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?

 A) 14 cms B) 21 cms C) 42 cms D) None of these

Explanation:

3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7

5.25 meters=525 cm = 5 × 5 × 3 × 7

Hence common factors are 3 and 7

Hence LCM = 3 × 7 = 21

Hence largest size of square tiles that can be paved exactly with square tiles is 21 cm.

Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability

25

Product of two co-prime numbers is 117. Their L.C.M  should be

 A) 1 B) 117 C) Equal to their H.C.F D) cannot be calculated

Explanation:

H.C.F of co-prime numbers is 1. So, L.C.M = $\inline&space;\fn_jvn&space;\frac{117}{1}$ =117

Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability

7

L.C.M of two prime numbers x and y (x>y) is 161. The value of 3y-x is :

 A) -2 B) -1 C) 1 D) 2

Explanation:

H. C. F of two prime numbers is 1.  Product of numbers = 1 x 161 = 161.

Let the numbers be a and b . Then , ab= 161.

Now, co-primes with  product 161 are (1, 161) and (7, 23).

Since x and y are prime numbers and x >y , we have x=23 and y=7.

$\inline&space;\fn_jvn&space;\therefore$ 3y-x = (3 x 7)-23 = -2

Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability

21

The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above condition is

 A) 4 B) 6 C) 8 D) 12

Explanation:

Let the required numbers be 33a and 33b.

Then 33a +33b= 528   $\inline&space;\fn_jvn&space;\Rightarrow$   a+b = 16.

Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).

$\inline&space;\fn_jvn&space;\therefore$ Required numbers are  ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)

The number of such pairs is 4
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