# Aptitude - HCF and LCM

### MCQ

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Q 21.

Find the value of X if HCF of X, 3240 and 3600 is 36 and their LCM is 24x35x52x72

Options:

• 22x35x72

• 25x52x72

• 23x35x72

• 22x53x72

Q 22.

Find GCD of 0.36, 0.9 and 1.08

Options:

• 0.18

• 0.90

• 0.108

• 0.27

Q 23.

Find the LCM of 22, 54, 108, 135 and 198

Options:

• 330

• 1980

• 5940

• 11880

Q 24.

Find the LCM of 24, 36 and 40

Options:

• 120

• 240

• 360

• 480

Q 25.

Find the HCF of

4x27x3125, 5x11x16x49x81 and 7x8x9x25

Options:

• 1260

• 540

• 180

• 360

Q 26.

Find the HCF of 3x5x7x11, 2x2x2x2x3x3x5x5x5x7 and 2x2x2x3x3x3x5x5x7x7

Options:

• 105

• 27720

• 2310

• 1155

Q 27.

Express 1095/1168 in simplest form

Options:

• 17/26

• 25/26

• 15/16

• 13/16

Q 28.

Express 252 as a product of primes

Options:

• 2x3x3x3x7

• 2x2x2x3x7

• 3x3x3x3x7

• 2x2x3x3x7

Q 29.

Jai and Veeru are running in opposite direction on a circular path at Eden Garden, Calcutta. Jai takes 5 minutes while Veeru takes 6 minutes to complete a lap. If they decided to run 6 laps then find the number of time they will cross each other.

Options:

• 1

• 2

• 3

• 4

Total time taken by Jai to complete a lap = 5 minutes

Total time taken by Veeru to complete a lap = 6 minutes

Total time taken by Jai to complete 6 laps = 5x6 = 30 minutes.

Total time taken by Veeru to complete 6 laps = 6x6 = 36 minutes.

HCF of 5 minutes and 6 minutes is 30 minutes.

So, they will cross only once.

Q 30.

Find the HCF of (x4 - y4) and (x6 - y6).

Options:

• x4 - y4

• x3 - y3

• x2 - y2

• x - y

f(x) = (x4 - y4)

= (x2)2 - (y2)2

= (x2 - y2)(x2 + y2)

= (x - y)(x + y)(x2 + y2)

g(x) = (x6 - y6)

= (x3)2 - (y3)2

= (x3 - y3)(x3 + y3)

= (x - y)(x2 - y2 + xy) (x + y)(x2 + y2 - xy)

= (x - y)(x + y) (x2 - y2 + xy)(x2 + y2 - xy)

Common factor in f(x) and g(x) = (x - y)(x + y) = (x2 - y2)

Therefore, HCF = (x2 - y2)

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