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 Ability

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.

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

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 |

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

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.

3y-x = (3 x 7)-23 = -2

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

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 a+b = 16.

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

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