H.C.F & L.C.M. - Online Quiz



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Questions and Answers

Q 1 - Find the lowest common multiple of 24, 36 and 40?

A - 120

B - 360

C - 240

D - 480

Answer : B

Explanation

L.C.M = 2 x 2 x 2 x 3 x 3 x 5 = 360

Q 2 - The G.C.D of 1.08, 0.36 and 0.9 is?

A - 0.108

B - 0.9

C - 0.03

D - 0.18

Answer : B

Explanation

Given numbers are 1.08, 0.36 and 0.9. H.C.F of 108, 36 and 90 is 18.
H.C.F of given numbers is 0.18.

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?

A - 1677

B - 2535

C - 1683

D - 3363

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?

A - 101

B - 111

C - 107

D - 185

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 - The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. the larger of the two number is?

A - 276

B - 299

C - 322

D - 345

Answer : C

Explanation

clearly the numbers are (23 x 13) and (23 x 14)
Larger number = (23 x 14) = 322.

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?

A - 35

B - 5

C - 6

D - 7

Answer : D

Explanation

The maximum possible length = (G.C.D. of 35, 42, 70) =7

Q 7 - Which greatest possible length can be used to measure exactly 165 cm, 330 cm and 440 cm.

A - 5

B - 15

C - 50

D - 55

Answer : D

Explanation

HCF of 165 cm, 330 cm and 440 cm is 55 cm.

Q 8 - If two numbers are greater than 13 and the H.C.F of two numbers be 13, L.C.M 273, then the sum of the numbers is:

A - 286

B - 130

C - 288

D - 290

Answer : B

Explanation

Let the number be 13 a and 13 b, where a and b are co-primes.
Then, 13a * 13b=   (13* 273)  ⇒ab= 21
Two co-primes with product 21are 3 and 7.
∴ numbers are (13*3, 13*7) i.e , 39 and 91.
Their sum = (39+91) = 130

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.

A - 35

B - 3/5

C - 4/3

D - 4/35

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 - What is the greatest length possible of a scale that can be used to measure exactly 7 m, 3 m 85 cm, 12 m 95 cm, is:

A - 15 cm

B - 25 cm

C - 35 cm

D - 42 cm

Answer : C

Explanation

Required length = H.C.F of 700 cm, 385 cm and 1295 cm= 35 cm
aptitude_hcf_lcm.htm
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