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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
Q 2 - The greatest number of four digits which is exactly divisible by 15, 25, 40, and 75 is?
Answer : C
Explanation
Greatest number of 4 digits is 9999. L.C.M of 15, 25, 400 and 75 is 600. On dividing 9999 by 600, the remainder is 399. Required number = (9999 - 399) = 9600.
Q 3 - 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?
Answer : C
Explanation
L.C.M of 5,6,7,8 = 840 Therefore Required number is of the form (840k + 3) Least value of k which (840k + 3) is divisible by 9 is k = 2. Therefore Required number = (840 x 2 + 3) = 1683
Q 4 - The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is?
Answer : B
Explanation
Let the numbers be 37a and 37b. then 37a x 37b = 4107 a x b = 3. Now, co-primes with product 3 are (1,3) So, the required numbers are (37 x 1, 37 x 3) i.e. (1, 111) Therefore greater number = 111.
Q 5 - L.C.M of two prime numbers a and b(a>b) is 161. The value of 3b - a is?
Answer : B
Explanation
H.C.F of two prime numbers is 1. Product of numbers = (1 x 161) = 161 Let the numbers be a and b. Then a x b = 161 now co-primes with product 161 are (1, 161) (7,23). Since a and b are prime numbers and a > b, we have a = 23 and b = 7. Therefore 3b - a = (3 x 7) - 23 = -2.
Q 6 - Three piece of timber 35m, 42m, 70m long have to be divided into planks of the same length. What is the greatest possible length of each cloth?
Answer : D
Explanation
The maximum possible length = (G.C.D. of 35, 42, 70) =7
Q 7 - A milk vendor has three kinds of milk: 68 litres, 119 litres and 153 litres. Find the least number of casks of equal size required to store all the milk without mixing.
Answer : B
Explanation
Size of the cask (G.C.D. of 68,119 and 153) =17 Number of casks =68/17+119/17+153/17=20
Q 8 - The H.C.F and L.C.M of two numbers is 11 and 7700. If one of the numbers is 275, find the other number:
Answer : C
Explanation
Let the other number be x. than , 11 * 7700 = 275 * X ⇒ x = (11* 7700)/275 = 308 Hence, the number is 308.
Q 9 - H.C.F and L.C.F of two numbers x and y are 3 and 105 respectively. If x+y=36 then figure out 1/x + 1/y.
Answer : D
Explanation
We have X *y =3 *105 ⇒ xy = 315 ∴ x+y/xy =36/315 = 4/35 ⇒ 1/y+1/x = 4/35 ⇒ 1/x+1/y = 4/35.
Q 10 - H.C.F of 3240, 3600 and x is 36 and their L.C.M is (2⁴*3⁵*52*72).Find x.
Answer : C
Explanation
3200 = 23* 3⁴*5 H.C.F = 36= 22*32 3600 = 2⁴*32* 52 L.C.M = 2⁴* 3⁵*52* 72 ∴ 3rd number must have 22*32 as its factor. ∴ 3rd number = 22* 3⁵*72