HCF and LCM (Part-2)

41. The sum of two numbers is 1224 and their HCF is 68. The number of pairs of numbers satisfying the above condition is: [SSC CPO 09/11/2022 (Afternoon)]

(a) 3
(b) 4
(c) 6
(d) 2

Correct Answer: (a) 3

Solution:

42. The LCM and ratio of three numbers are 1386 and 3 : 7 : 11, respectively. The sum of the greatest and least numbers is: [SSC CPO 11/11/2022 (Evening)]

(a) 60
(b) 64
(c) 84
(d) 108

Correct Answer: (c) 84

Solution:

43. If P = 2⁸ × 3⁵ × , Q = 2³ × 3⁴, and R = 3⁵ × 2⁷, then what is the highest common factor of P, Q and R?

(a) 2³ × 3⁴
(b) 2⁸ × 3⁵
(c) 2² × 3²
(d) 2⁴ × 3⁵

Correct Answer: (a) 2³ × 3⁴

Solution:

44. The ratio of the LCM of two numbers to the sum of the same two numbers is 12 : 7. If their HCF is 4, what is the product of these two numbers? [SSC MTS 14/07/2022 (Morning)]

(a) 192
(b) 172
(c) 196
(d) 160

Correct Answer: (a) 192

Solution:

45. If K₁ and K₂ are two distinct prime numbers, then what is the product of the highest common factor and the least common multiple of K₁ and K₂? [SSC MTS 20/07/2022 (Afternoon)]

Correct Answer: (d)

Solution:

46. Find the smallest natural number 'x' that must be subtracted from 1800 so that (1800x), when divided by 7, 11 and 23, will leave 5 as the remainder in each case. [SSC MTS 26/07/2022 (Evening)]

(a) 24
(b) 25
(c) 26
(d) 20

Correct Answer: (a) 24

Solution:

LCM of 7, 11 and 23 = 1771
Remainder in each case = 5
So, required number = 1771 + 5 = 1776
Value of x = 1800 - 1776 = 24

47. Four runners started running simultaneously from a point on a circular track. They took 400 seconds, 600 seconds, 720 seconds and 900 seconds to complete one round. After how much time did they meet at the starting point for the first time since the race started? [SSC CHSL 03/06/2022 (Morning)]

(a) 4200 sec
(b) 2400 sec
(c) 3600 sec
(d) 1800 sec

Correct Answer: (c) 3600 sec

Solution:

48. Which is the smallest multiple of 7, which leaves 5 as a remainder in each case, when divided by 8, 9, 12 and 15? [SSC CGL 12/04/2022 (Morning)]

(a) 365
(b) 1085
(c) 2525
(d) 725

Correct Answer: (b) 1085

Solution:

49. Three numbers are in the ratio 1/2 : 2/3 : 3/4. If the difference between the greatest number and the smallest number is 33, then HCF of the three numbers is: [SSC CGL Tier II (03/02/2022)]

(a) 9
(b) 5
(c) 13
(d) 11

Correct Answer: (d) 11

Solution:

50. The least number of square tiles required to pave the ceiling of a room 12 m 95 cm long and 3 m 85 cm broad, is: [SSC MTS 11/10/2021 (Afternoon)]

(a) 417
(b) 407
(c) 467
(d) 437

Correct Answer: (b) 407

Solution:

HCF and LCM (Part-2)

41. The sum of two numbers is 1224 and their HCF is 68. The number of pairs of numbers satisfying the above condition is: [SSC CPO 09/11/2022 (Afternoon)]

42. The LCM and ratio of three numbers are 1386 and 3 : 7 : 11, respectively. The sum of the greatest and least numbers is: [SSC CPO 11/11/2022 (Evening)]

43. If P = 2⁸ × 3⁵ × , Q = 2³ × 3⁴, and R = 3⁵ × 2⁷, then what is the highest common factor of P, Q and R?

44. The ratio of the LCM of two numbers to the sum of the same two numbers is 12 : 7. If their HCF is 4, what is the product of these two numbers? [SSC MTS 14/07/2022 (Morning)]

45. If K₁ and K₂ are two distinct prime numbers, then what is the product of the highest common factor and the least common multiple of K₁ and K₂? [SSC MTS 20/07/2022 (Afternoon)]

46. Find the smallest natural number 'x' that must be subtracted from 1800 so that (1800x), when divided by 7, 11 and 23, will leave 5 as the remainder in each case. [SSC MTS 26/07/2022 (Evening)]

47. Four runners started running simultaneously from a point on a circular track. They took 400 seconds, 600 seconds, 720 seconds and 900 seconds to complete one round. After how much time did they meet at the starting point for the first time since the race started? [SSC CHSL 03/06/2022 (Morning)]

48. Which is the smallest multiple of 7, which leaves 5 as a remainder in each case, when divided by 8, 9, 12 and 15? [SSC CGL 12/04/2022 (Morning)]

49. Three numbers are in the ratio 1/2 : 2/3 : 3/4. If the difference between the greatest number and the smallest number is 33, then HCF of the three numbers is: [SSC CGL Tier II (03/02/2022)]

50. The least number of square tiles required to pave the ceiling of a room 12 m 95 cm long and 3 m 85 cm broad, is: [SSC MTS 11/10/2021 (Afternoon)]

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