Problems On Hcf And Lcm

The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:

A:

504

B:

536

C:

544

D:

548

Answer: D

Required number = (L.C.M. of 12, 15, 20, 54) + 8

= 540 + 8

= 548.

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Which of the following fraction is the largest ?

A:

7

8

B:

13

16

C:

31

40

D:

63

80

Answer: A

L.C.M. of 8, 16, 40 and 80 = 80.

7	=	70	;	13	=	65	;	31	=	62
8	=	80	;	16	=	80	;	40	=	80

Since,	70	>	65	>	63	>	62	, so	7	>	13	>	63	>	31
	80		80		80		80		8		16		80		40

So,	7	is the largest.
	8

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Find the highest common factor of 36 and 84.

A:

4

B:

6

C:

12

D:

18

Answer: C

36 = 2² x 3²

84 = 2² x 3 x 7

H.C.F. = 2² x 3 = 12.

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Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:

A:

75

B:

81

C:

85

D:

89

Answer: C

Since the numbers are co-prime, they contain only 1 as the common factor.

Also, the given two products have the middle number in common.

So, middle number = H.C.F. of 551 and 1073 = 29;

First number =		551		= 19; Third number =		1073		= 37.
		29				29

Required sum = (19 + 29 + 37) = 85.

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The greatest possible length which can be used to measure exactly the lengths 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

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

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Questions for: Problems On Hcf And Lcm