problems on hcf and lcm – Free Online Questions and Answers

21.

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 & Explanation

Answer: Option C

Explanation:

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

22.

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 & Explanation

Answer: Option C

Explanation:

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.

23.

Find the highest common factor of 36 and 84.

A.	4	B.	6
C.	12	D.	18

Answer & Explanation

Answer: Option C

Explanation:

36 = 2² x 3²

84 = 2² x 3 x 7

H.C.F. = 2² x 3 = 12.

24.

Which of the following fraction is the largest ?

Answer & Explanation

Answer: Option A

Explanation:

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

25.

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 & Explanation

Answer: Option D

Explanation:

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

= 540 + 8

= 548.