# HCF and LCM ( 16 to 20 )

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Questions:

16. The least number which when divided by 14, 18, 27 and 54 leaves in each case a remainder of 8 is:

A)    504

B)    536

C)    544

D)    386

E)    None of these

Explanation:

LCM of (14, 18, 27 and 54) = 378

Required Number = 378 + 8 = 386

17. The least multiple of 7, which leaves a remainder of 4 when divided by 8, 12, 18 and 27 is:

A)    74

B)    494

C)    384

D)    868

E)    None of these

Explanation:

LCM of (8, 12, 18 and 27) = 216

Let required number be 216k + 4 which is a multiple of 7

Least value of k for which (216k + 4) is divisible by 7 is k = 4

∴ required number = 216 * 4 + 4 = 868

18. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 42 seconds, B in 70 seconds and C in 65 seconds, all starting at the same point. At what time will they meet again at the beginning point?

A)    26mins 18secs

B)    42mins 36secs

C)    45mins 30secs

D)    46mins 12secs

E)    None of these

Explanation:

LCM of (42, 70 and 65) = 2730

So, A, B and C will again meet at the starting point in 2730secs i.e. 45mins 30secs.

19. Which of the following fractions is the largest?

A)

$\frac{3}{4}$

B)

$\frac{7}{8}$

C)

$\frac{13}{16}$

D)

$\frac{31}{40}$

E) None of these

Explanation:

LCM of 4, 8, 16 and 40 = 80

20. The greatest number that exactly divides 105, 1001 and 2436 is:

A)    3

B)    7

C)    11

D)    21

E)    None of these

Explanation:

HCF of (1001 and 2436) = 7

HCF of (105 and 7) = 7

∴ HCF of 105, 1001 and 2436 = 7