H.C.F and L.C.M- Aptitude Questions and Answers

 Find the largest five digits number that is divisible by 7, 10, 15, 21 and 25? A) 98700 B) 98950 C) 99750 D) None of these Correct Answer :99750 Explanation :The least number which is exactly divisible by 7, 10, 15, 21 and 25 is their L.C.M, i.e. L.C.M of 7, 10, 15, 21 and 25 =1050 The Largest number of five digits is 99999. Required number must be divisible by L.C.M of 7, 10, 15, 21 and 25 i.e. 1050 On dividing 99999 by 1050 get 249 as remainder. So required number is = (99999-249) = 99750. How many possible pairs of numbers exist whose product is 5400 and HCF is 30? A) 1 B) 2 C) 3 D) 4 Correct Answer :2 Explanation :H.C.F of numbers is 30 So required numbers should be multiple of 30. lets the numbers are 30a and 30b ,there the product of the numbers = 5400 Then, 30a * 30b = 5400 <=> ab = 6 the co-primes or possible pairs of product 6 either (1, 6) and (2,3), or (6,1) and (3, 2) that means a*b=6 30a*30b = 5400 30*180 = (30,180) = 5400 (there (1, 6) a=1 , b=6) 60*90 = (60,90) = 5400 (there (2, 3) a=2 , b=3) thus,two numbers of pairs are possible whose product is 5400 and H.C.F. is 30. The HCF and LCM of two numbers are 8 and 48 respectively. If one of the numbers is 24, then the other number is? A) 48 B) 36 C) 24 D) 16 Correct Answer :16 Explanation :lets other number is Z as per rule, Product of two numbers =Product of their H.C.F. and L.C.M So Z*24=8*48 Z=384/24 => 16 Three bells toll at interval of 36 seconds, 40 seconds and 48 seconds respectively. They started ringing together at particular time. They next toll together after? A) 12 min B) 6 min C) 24 min D) 18 min Correct Answer :12 min Explanation :Least common multiples (LCM) of Interval of bells toll: = (36 to 40 to 48)/2 = (18 to 20 to 24)/2 = (9 to 10 to 12)/2 = (9 to 5 to 6)/3 = (3 to 5 to 2) So,They will start ringing together again after: = (2 * 2 * 2 * 3 * 3 * 5 * 2) sec = 720 sec Thus , next toll together after 720 sec i.e. 12 mins Three wheels can complete 60, 36, 24 revolutions per minute respectively. There is red mark on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again? A) 2.5 second B) 1.6 second C) 5 second D) 7.5 second Correct Answer :5 second Explanation :The first wheel spins at 60 rpm which means that it completes 60/60 = 1 revolution every second. The second wheel spins at 36 rpm. So it completes 36/60 = 0.6 of a revolution every second The third wheel spins at 24 rpm. So it completes 24/60 = 0.4 of a revolution every second. So we have the values: 1, 0.6, 0.4 If we wait 10 seconds, then we multiply each value by 10 to get: 10, 6, 4 Now we can divide by the GCF 2 to get 5, 3, 2 This means that it will take 5 seconds for the spots to line up again (since the first number corresponds to the amount of time that has gone by in seconds) Find the HCF of the numbers a and b, where a = 25*32*76*114 and b = 23*34*56*11*133 ? A) 396 B) 408 C) 792 D) 1584 Correct Answer :792 Explanation :HCF is the product of all common prime factors using the least power of each common prime factor HCF = 23 x 32 x 11 = 792 What is the least number of that is exactly divisible by 4, 12, 15, and 18? A) 120 B) 108 C) 180 D) 240 Correct Answer :180 Explanation :The least number which is exactly divisible by is their LCM of (4, 12, 15, and 18) =4,12,15,18|2 =2,6,15,9|3 =2,2,5,3|2 =1,1,5,3 LCM=2*3*2*1*5*3=180 The HCF of 2 numbers is 11 and LCM is 693.If one of numbers is 77.find the other number ? A) 99 B) 198 C) 66 D) 143 Correct Answer :99 Explanation :Product of two numbers = Product of their HCF and LCM 77 x a = 11 x 693 Other number a = 11 x 693 / 77 =99. The largest number , which exactly divides 210, 315, 147 and 168 is ? A) 3 B) 7 C) 21 D) 4410 Correct Answer :21 Explanation :The largest number is the H.C.F. of 210, 315, 147, and 168, which is 21. The H.C.F and L.C.M of two number are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is ? A) 33 B) 66 C) 132 D) 264 Correct Answer :132 Explanation :Product of two numbers = Product of their HCF and LCM. First number = 2 x 44 = 88 Second number = (LCM x HCF ) / First number So, Second number = 44 x 264 / 88 = 132. Find the HCF of 22 * 32, 2 * 34 * 7 ? A) 128 B) 126 C) 146 D) 434 Correct Answer :126 Explanation :22 * 32 =>2*2*3*3 2 * 34 * 7=>2*3*3*3*3*7 HCF is the product of all common prime factors using the least power of each common prime factor. So we got 2*3*3*7 = 126 Find the HCF of 54, 288 and 360 ? A) 18 B) 36 C) 54 D) 72 Correct Answer :18 Explanation :Let’s solve this question by factorization method. 54 =2 * 33 288 = 25 * 32 360 = 23 * 32 * 5 So HCF is the product of all common prime factors using the least power of each common prime factor in all three, i.e. 2 * 3² =18