# 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.

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Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic AbilityThe G.C.D of 1.08, 0.36 and 0.9 is

A) 0.03 | B) 0.9 |

C) 0.18 | D) 0.108 |

Explanation:

Given numbers are 1.08 , 0.36 and 0.90

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

H.C.F of given numbers = 0.18

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

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

Explanation:

Let the numbers 13*a* and 13*b*.

Then, 13*a* x 13*b* = 2028

*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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Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic AbilityIf the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:

A) 55/601 | B) 601/55 |

C) 11/120 | D) 120/11 |

Explanation:

Let the numbers be *a* and *b*.

Then, *a* + *b* = 55 and *ab* = 5 x 120 = 600.

The required sum =(1/a)+(1/b)=(a+b)/ab=55/600=11/120

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