H.C.F & L.C.M. - Online Quiz
Following quiz provides Multiple Choice Questions (MCQs) related to H.C.F & L.C.M.. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.
Answer : A
Explanation
108 = 23 x 33 288 = 25 x 32 360 = 23 x 32 x 5 Therefore H.C.F = 2 2 x 32 = 36
Q 2 - Three numbers are in the ratio 1:2:3 and their H.C.F is 12. The numbers are?
Answer : B
Explanation
Let the required numbers be z, 2z, and 3z. Then, their H.C.F = z So, z = 12. Therefore The number are 12, 24 and 36.
Q 3 - The least multiple of 7, which leaves a remainder 4, when divided by 6,9,15 and 18 is?
Answer : A
Explanation
L.C.M of 6,9,15 and 18 is 90. Let required number be 90k + 4, which is a multiple of 7. Least value of k for which (90k + 4) is divisible by 7 is k = 4. Therefore Required number 90 x 4 + 4 = 364.
Q 4 - The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is?
Answer : B
Explanation
Other number = 11 x 7700⁄275 = 308
Q 5 - Find the greatest number that will divide 43, 91, and 183 so as to leave the same remainder in each case.
Answer : C
Explanation
Required number = H.C.F of (91 - 43), (183 - 12) and (183 - 43) = H.C.F of 48, 92, and 140 = 4
Answer : A
Explanation
L.C.M. of given fractions = (L.C.M.of numerators)/(H.C.F.of denominators)=2/1=2 (L.C.M.of numerators = 2 H.C.F.of denominators =1)
Q 7 - H.C.F. of two numbers is 12 and their L.C.M is 72. If the difference between the numbers is 24, their sum is
Answer : C
Explanation
Let the numbers be X & Y HCF*LCM=Product of two numbers =XY=12x72=864 XY=864 -------- (1) Given X-Y=24 -------- (2) On solving 1 & 2 we get X=12 Y=36 Their sum = 12+36=48
Q 8 - Having H.C.F and L.C.M of two numbers as 21 and 4641 respectively. If one of the numbers is in between 200 and 300, then the two numbers are :
Answer : D
Explanation
Let the numbers be 21 a and 21 b, where a and b are co-primes. Then ,21 a* 21 b= (21* 4641)⇒ab= 221. Two co-primes with product 221 are 13 and 17. ∴ Numbers are (21*13, 21*17) , i.e (273,357)
Q 9 - If ratio of two numbers is 2:3 and the product of their H.C.F and L.C.M is 33750, find the sum of the numbers:
Answer : C
Explanation
Let the numbers be 2x and 3x. Then, H.C.F = x and L.C.M = 6x ∴ 6x*x = 33750 ⇒ x2 = 5625 ⇒ &sqrt;5625= 75 So, the numbers are 150 and 225 . Their sum is 375.
Answer : C
Explanation
210 = 2*3*5*7, 315 =3*5*3*7 , 147 = 7*7*3 , 168 = 2*2*2*3*7 Required number = H.C.F of given numbers= (3*7) =21
