# L.C.M and H.C.F.

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## Practice Questions on LCM and HCF

 Q26) There are 3 bells. First bell tolls every 39 seconds, second bell tolls every 65 seconds and the third bell tolls every 75 seconds. The bells start tolling together at 8:00 AM. At what time will the three bells toll together again? 1) 8:16:25 AM2) 8:16:15 AM3) 8:10:15 AM4) 9:37:30 AM The three bells will toll together after L.C.M.(39,65,75) = 975 sec i.e.8:16:15 AM Hence, option 2. Q27) A farmer has 407 apples, 592 bananas and 888 oranges. He wants to store these fruits into boxes of equal size without mixing the fruits. How many fruits can be stored in a box if minimum number of boxes are to be used? 1) 372) 273) 514) 40 H.C.F.of 407, 592, 888 = 37 Hence, option 1. Q28) If HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n =72 then is equal to 1) 1/35 2) 3/35 3) 5/37 4) 2/35 Hence, option 4. Q29) The product of two whole numbers is 1500 and their HCF is 10. Find the L.C.M. 1) 15000 2) 150 3) 1500 4) None of these Product of numbers = LCM×HCF LCM = 1500/10 = 150 Hence, option 2. Q30) The LCM of two numbers is 20 times of their HCF and (LCM + HCF) = 2520. If one number is 480, what will be the triple of another number? 1) 1800 2) 600 3) 1200 4) None of these Let HCF be x. According to the question, LCM = 20x LCM + HCF = 2520 21x = 2520 x = 120 LCM = 20×120 = 2400 Number-1 × Number-2 = 2400×120 Number-2 = 2400 × 120/480 = 600 Required answer = 3×600 = 1800 Hence, option 1. Q31) 2 pieces of cakes of weights 253gms and 368gms are to be divided into equal parts. Each part must be as heavy as possible. If one such part is served to each guest, then what is the weight of each piece of cake such that minimum number of guests that could be served. 1) 162) 113) 234) 27 Weight of a piece of cake = H.C.F.(253,368) = 23 Hence, option 3.