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
Answer & Explanation Answer: B) 127

Explanation:

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


  = H.C.F. of 1651 and 2032 = 127.

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

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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
Answer & Explanation Answer: B) 117

Explanation:

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

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

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The G.C.D of 1.08, 0.36 and 0.9 is

A) 0.03 B) 0.9
C) 0.18 D) 0.108
Answer & Explanation Answer: C) 0.18

Explanation:

Given numbers are 1.08 , 0.36 and 0.90


H.C.F of 108, 36 and 90 is 18                  [ \inline \fn_jvn \because G.C.D is nothing but H.C.F]


\inline \fn_jvn \therefore H.C.F of given numbers = 0.18                 

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

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The H.C.F and L.C.M of two numbers are 11 and 385 respectively. If one number lies between 75 and 125 , then that number is

A) 77 B) 88
C) 99 D) 110
Answer & Explanation Answer: A) 77

Explanation:

Product of numbers = 11 x 385 = 4235


Let the numbers be 11a and 11b . Then , 11a x 11b = 4235  \inline \fn_jvn \Rightarrow  ab = 35


Now, co-primes with product  35 are (1,35) and (5,7)


So, the numbers are ( 11 x 1, 11 x 35)  and (11 x 5, 11 x 7)


Since one number lies 75 and 125, the suitable pair is  (55,77)


Hence , required number = 77

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The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

A) 1 B) 2
C) 3 D) 4
Answer & Explanation Answer: B) 2

Explanation:

Let the numbers 13a and 13b.


Then, 13a x 13b = 2028


{\color{Blue} \Rightarrow }ab = 12.


Now, the co-primes with product 12 are (1, 12) and (3, 4).


[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]


So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).


Clearly, there are 2 such pairs.

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