lcm and hcf Model Questions & Answers, Practice Test for ssc mts paper 1 2023

Answer: (a)

The maximum number of boys or girls alone in a group will be equal to the H.C.F. of 264 and 408.

= 24

Answer: (d)

Since each rod must be cut into parts of equal length and each part must be as long as possible, so HCF should be taken.

HCF of 78, 104, 117 and 169 = 13.

No. of parts from 78cm. rod = $78/13$ = 6

No. of parts from 104 cm. rod = $104/13$ = 8

No. of parts from 117 cm. rod = $117/13$ = 9

No. of parts from 169 cm. rod = $169/13$ = 13.

∴Maximum no. of pieces = 6 + 8 + 9 + 13 = 36

Answer: (c)

Clearly, the required number must be greater than the LCM of 18, 24, 30 and 42 by 1.

Now, 18 = 2 × $3^2$

24 = $2^3$ × 3

30 = 2 × 3 × 5

42 = 2 × 3 × 7

∴ LCM = $3^2 ×2^3$ × 5 × 7 = 2520

∴ the required number = 2520 + 1 = 2521

Answer: (b)

Clearly, HCF is 1

Answer: (a)

Let the numbers be x and 4x.

Then, 84 ×21=x×4x

or $4x^2$=1764

or $x^2$= 441 or x = 21

⇒ 4x = 4 × 21 = 84

Thus the larger number = 84