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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.
Q 1 - 252 can be expressed as a product of primes as
Answer : B
Explanation
Clearly, 252 = 2 x 2 x 3 x 3 x 7.
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 sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is?
Answer : A
Explanation
Let the numbers be 33a and 33b. then 33a + 33b = 528 a + b = 16. Now, co-primes with product 16 are (1,15) (3,13) (5,11) and (7,9) So, the required numbers are (33 x 1, 33 x 15) (33 x 3, 33 x 13) (33 x 5, 33 x 11) (33 x 7, 33 x 9) the number of such pairs is 4.
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 - Two numbers, both greater than 29, have H.C.F 29 and L.C.M 4147. the sum of the numbers is?
Answer : B
Explanation
Product of numbers = 29 x 4147. let the numbers be 29a and 29b. then 29a x 29b = (24 x 4147) = ab = 143 Now co-primes with product 143 are (1, 143) (11, 13). So the numbers are (29 x 1, 29 x 143) and (29 x 11, 29 x 13). Since both numbers are greater than 29 the suitable pair (29 x 11, 29 x 13) i.e (319, 377). Required sum = (319 + 377) = 696.
Answer : B
Explanation
H.C.F. of given fractions = (H.C.F.of denominators)/(L.C.M.of numerators)=2/105 ( H.C.F.of numerators = 2 L.C.M.of denominators =105)
Q 7 - The ratio between the LCM and HCF of two numbers is 12:1. If the numbers be 48 and 64, find their LCM and HCF.
Answer : A
Explanation
Let the LCM & HCF be 12X & X respectively LCM x HCF =12X x X=48x64 ⇒X2= (48x64)/12⇒X=16 ⇒HCF=16 & LCM=192
Q 8 - H.C.F and L.C.M of two 3-digit numbers are 29 and 4147 respectively. What is the sum of the numbers?
Answer : C
Explanation
Let the numbers be 29a and 29 b , where a and b are co-primes. Then, 29 a * 29 b + 29*147 ⇒ ab + (29*4147)/(29*29)= 143 co-primes with product 143 are 11 and 13. ∴ numbers are (29*11, 29* 13) i.e , 319, 377 Their sum = (319+377)= 696
Q 9 - Having two numbers in the ratio 5:7 and their L.C.M as 315, then their product is:
Answer : A
Explanation
Let the two numbers be 5x and 7x . Then, their L.C.M is 35 x. 35x = 315 ⇒ x= 9 ∴ The numbers are 45 and 63 and their product is 2835.
Q 10 - If the H.C.F of two numbers is 24 then number which can be their L.C.M is:
Answer : B
Explanation
H.C.F always divides L.C.M completely. ∴ L.C.M is 120.