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

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Questions and Answers

Q 1 - Reduce 128352⁄238368 to its lowest terms.

A - 7⁄13

B - 3⁄4

C - 5⁄13

D - 9⁄13

Answer : A

Explanation

Q 2 - Which of the following fractions is the largest?

A - 7⁄8

B - 13⁄16

C - 31⁄40

D - 63⁄80

Answer : A

Explanation

L.C.M of 8, 16, 40 and 80 = 80
7⁄8 = 70⁄80; 13⁄16 = 65⁄80; 31⁄40 = 62⁄80
Since 70⁄80 > 63⁄80 > 65⁄80 > 62⁄80
7⁄8 > 63⁄80 > 13⁄16 > 31⁄40
S0, 7⁄8 is the largest.

Q 3 - The least multiple of 7, which leaves a remainder 4, when divided by 6,9,15 and 18 is?

A - 630

B - 364

C - 360

D - 540

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 - If the sum of two numbers is 55 and the H.C.F and L.C.M of these numbers are 5 and 120 respectively then the sum of the reciprocals of the numbers is equal to?

A - 11⁄120

B - 55⁄601

C - 601⁄55

D - 120⁄11

Answer : A

Explanation

Let the numbers be a and b. Then a + b = 55 and a x b = 5 x 120 = 600
therefore Required sum = 1⁄a + 1⁄b = a + b⁄a x b
55⁄600 = 11⁄120

Q 5 - Let N be the greatest number that will divide 1305, 4665 and 6905 leaving the same remainder in each case. then the sum of the digits in N is?

A - 5

B - 4

C - 6

D - 8

Answer : B

Explanation

N = H.C.F of (4665 - 1305), (6905 - 4665), (6905 - 1305)
= H.C.F of 3360, 2240 and 5600 = 1120.
Sum of digits in N = (1 + 1 + 2 + 0) = 4.

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 - Find the greatest possible rate at which a man should walk to cover a distance of 35 km and 140 km in exact number of days

A - 30

B - 70

C - 25

D - 35

Answer : D

Explanation

GCD of two 35 and 140=35

Q 8 - The L.C.M and H.C.M of two numbers is 2310 and 30. If one of these numbers is 210, what is the second number?

A - 330

B - 1470

C - 2100

D - 16170

Answer : A

Explanation

Let the second number be x. Then,
2310 * 30  = 210 *x ⇒x = (2310 *30)/210 =  330
∴ the second number is 330.

Q 9 - If the sum of two numbers is 216 and H.C.F is 27. Find the numbers:

A - 54, 162

B - 108, 108

C - 27, 189

D - none of these

Answer : C

Explanation

let the numbers be 27 a and 27 b.
Then, 27 a +27 b= 216  ⇒ a+b = 216/27 = 8
co-primes with sum 8 are (1,7 ) and (3,5)
So, the numbers are (27*1, 27*7) or (27*3, 27*5)
i.e (27 and 189) or (81 and 135).
Out of the given numbers , the right choice  is 27, 189.

Q 10 - If the product of two co-primes is 117 then their L.C.F should be

A - 1

B - 117

C - equal to their H.C.F

D - cannot be calculated

Answer : B

Explanation

H.C.F of co-primes=1
H.C.F * L.C.M = Their product = 117
∴ 1* L.C.M = 117 ⇒L.C.M = 117

aptitude_hcf_lcm.htm
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