H C F and L C M Questions and Answers Quiz 1

1 . 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 2 . The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 275, then the other is A.   279 B.   283 C.   308 D.   318 3 . The product of two numbers is 4107. If the HCF of those numbers is 37, then the greater number is A.   101 B.   107 C.   109 D.   111 4 . The greatest possible length which can be used to measure exactly the length 7m, 3m, 85cm, 12m, 95 cm is A.   15 cm B.   25 cm C.   35 cm D.   42 cm 5 . Find the greatest number that will divide 43, 91 and 183 so as to leave the same remained in each case. A.   4 B.   7 C.   9 D.   13 6 . 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 7 . Three numbers are in the ration 1 : 2 : 3 and their HCF is 12. The numbers are A.   4,8,12 B.   5,10,15 C.   10,20,30 D.   12,24,36 8 . A rectangular courty 3.78 metres long and 5.25 metres 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.   Data inadequate 9 . The product of two numbers is 1320 and their HCF is 6. The LCM of the numbers is A.   220 B.   1314 C.   1326 D.   7920 10 . Product of two co-prime numbers is 117. Their LCM should be A.   1 B.   117 C.   equal to their H.C.F. D.   Cannot be calculated

Answers & Solutions   1 .     Answer : Option B Explanation : Required numbers = (LCM of 12, 16, 18, 21, 28) + 7 = 1008 + 7 = 1015 2 .     Answer : Option C Explanation : Other number = [11 ×$7700\over275$ ] = 308 3 .     Answer : Option D Explanation : Let the numbers be 37a and 37b. Then, 37a × 37b = 4107 ab = 3 Now, co-primes with product 3 are (1, 3) So, the required numbers are (37 × 1, 37 × 3) i.e., (1, 111) Therefore greater number = 111 4 .     Answer : Option C Explanation : Required length = HCF of 700 cm, 385 cm and 1295 cm = 35 cm 5 .     Answer : Option A Explanation : Required number = HCF of (91 - 43), (183 - 91) and (183 - 43) = HCF of 48, 92 and 140 = 4 6 .     Answer : Option C Explanation : Given numbers are 1.08, 0.36 and 0.90 HCF of 108, 36 and 90 is 18 HCF of given numbers – 0.18 7 .     Answer : Option D Explanation : Let the required numbers be x, 2x and 3x The, their HCF = x, So x = 12 The numbers are 12, 24, 36 8 .     Answer : Option B Explanation : Largest size of the tile. HCF of 378 cm and 525 cm = 21 cms. 9 .     Answer : Option A Explanation : LCM = $Product\,\, of \,\,numbers \over HCF$ =$1320\over6$ =220 10 .     Answer : Option B Explanation : HCF of co-prime numbers is 1 So, LCM = $117\over1$= 117