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

### The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is

 A) 1677 B) 1683 C) 2523 D) 3363

Explanation:

L.C.M of 5, 6, 7, 8 = 840

$\inline&space;\fn_jvn&space;\therefore$ Required Number is of the form 840k+3.

Least value of k for which (840k+3) is divisible by 9 is k = 2

$\inline&space;\fn_jvn&space;\therefore$  Required  Number = (840 x 2+3)=1683

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

### The smallest number which when diminished by 7,  is divisible by  12, 16, 18, 21 and 28 is

 A) 1008 B) 1015 C) 1022 D) 1032

Explanation:

Required Number = (L.C.M  of 12, 16, 18,21,28)+7 = 1008 + 7 = 1015

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

### Find the Greatest Number that will devide 43, 91  and 183  so as to leave the same remainder in each case

 A) 4 B) 7 C) 9 D) 13

Explanation:

Required Number = H.C.F  of  (91- 43), (183- 91) and (183-43)

= H.C.F of 48, 92, and 140 = 4

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:

Largest size of the tile  = H.C.F of 378 cm and 525 cm = 21 cm

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

### The maximum number of students  among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:

 A) 91 B) 910 C) 1001 D) 1911