### HCF and LCM Questions and Answers

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Q 1
2 gears one with 12 teeth and another with 14 teeth are engaged with each other. One tooth in smaller and one tooth in bigger are marked and initially those 2 marked teeth are in contact with each other. After how many rotations of the smaller gear, will the marked teeth in the two gears come into contact for the first time?

A)   7

B)   12

C)   84

D)   Data Insufficient

Correct Option - A

ExplanationLet the distance between two teeth be 1 cm. Circumference of first gear = 12 cm Circumference of second gear = 14 cm LCM(12,14) = 84 To cover 84 cm, no. of rotations taken by the first gear = 84/12 = 7

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Q 2
The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is

A)   74

B)   94

C)   184

D)   364

Correct Option - D

ExplanationLCM(6,9,15,18) = 90 The number is of the form 90x+4. 90x+4 should be a multiple of 7. By trial and error method, x=1 94 not divisible by 7. x=2 184 not divisible by 7. x=3 274 not divisible by 7. x=4 364 is divisible by 7. Hence, the number is 364.

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Q 3
The largest number which when divided by 10, 13 and 21 leaves 5 as the remainder in each case is

A)   2735

B)   915

C)   1295

D)   3145

Correct Option - A

ExplanationUsing the formula, the least number which when divided by two numbers x and y, leaving the same remainder z in each case is LCM(x,y) + z LCM(10,13,21) = 2730 2730+5=2735

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Q 4
The HCF and LCM of two numbers are 4 and 60. Which of the following could be those numbers?

A)   24,60

B)   6,40

C)   12,20

D)   18,40

Correct Option - C

ExplanationProduct of the numbers = 4*60 = 240 Only the options B and C satisfy this. HCF(6,40) = 2 HCF(12,20) = 4 Hence, the numbers are 12 and 20.

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Q 5
The H.C.F. of two numbers is 19 and their L.C.M. is 114. If one of the numbers is 57, find the other number.

A)   228

B)   114

C)   95

D)   38

Correct Option - D

ExplanationProduct = 19*114 Other number = 19*114/57 = 38

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Q 6
The HCF of two positive integers is 24. Which of the following cannot be their LCM?

A)   180

B)   312

C)   240

D)   168

Correct Option - A

ExplanationThe LCM has to be a multiple of HCF. 180 is not divisible by 24. Hence, 180 cannot be the LCM.

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Q 7
The least multiple of 7 which leaves a remainder 4 when divided by 6,9,15 and 18 is

A)   214

B)   91

C)   364

D)   637

Correct Option - C

ExplanationLCM(6,9,15,18) = 90 The number should be a multiple of 7 and of the form 90k+4. k=1, n=94 k=2, n=184 k=3, n=274 k=4, n=364 364 is a multiple of 7.