Question 1

Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

Accepted Answer

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

Question 2

If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:

Accepted Answer

Let the numbers be a and b Then, a + b = 55 and ab = 5 x 120 = 600. ∴ The required sum = 1 + 1 = a + b = 55 = 11 a b ab 600 120

Question 3

The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

Accepted Answer

Let the numbers be 37 a and 37 b Then, 37a x 37b = 4107 ⟹ ab = 3. Now, co-primes with product 3 are (1, 3). So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111). ∴ Greater number = 111.

Question 4

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:

Accepted Answer

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.

Question 5

Which of the following fraction is the largest?

Accepted Answer

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

Question 6

The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:

Accepted Answer

Required number = (L.C.M. of 12, 15, 20, 54) + 8 = 540 + 8 = 548.

Question 7

Which of the following has the most number of divisors?

Accepted Answer

99 = 1 x 3 x 3 x 11 101 = 1 x 101 176 = 1 x 2 x 2 x 2 x 2 x 11 182 = 1 x 2 x 7 x 13 So, divisors of 99 are 1, 3, 9, 11, 33, .99 Divisors of 101 are 1 and 101 Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176 Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Hence, 176 has the most number of divisors.

Question 8

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

Accepted Answer

Clearly, the numbers are (23 x 13) and (23 x 14). ∴ Larger number = (23 x 14) = 322.

Question 9

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

Accepted Answer

Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032 = 127.

Question 10

The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:

Accepted Answer

Other number = ❨ 11 x 7700 ❩ = 308. 275

Question 11

What is the greatest number that divides 263, 935 and 1383 leaving a remainder of 7 in each case?

Accepted Answer

The required greatest number is the HCF of 263-7, 935-7, 1383-7 i.e. 256, 928 and 1376 HCF = 32

Question 12

If (x+2) is the HCF of x 2 + ax + b and x 2 + cx + d , then which one of the following is correct?

Accepted Answer

If (x+2) is the HCF of x2 + ax + b and x2 + cx + d. Then, (-2)2 -2a +b = (-2)2 -2c + d b + 2c = 2a + d

Question 13

Find the greatest possible length which can be used to measure 4m 3cm, 4m 34cm and 4m 65cm exactly.

Accepted Answer

Required measure = HCF of 403, 434 and 465 = 31 cm

Question 14

Which of the following fractions is the greatest of all? 7/8, 6/7, 4/5, 5/6?

Accepted Answer

7 / 8 = 0.875, 6 / 7 = 0.857, 4 / 5 = 0.8 and 5/6 = 0.833 Now, 0.875 > 0.857 > 0.833 > 0.8 So, 7/8 is the greatest

Question 15

L.C.M of 2/3, 4/9, 5/6 and 7/12 is?

Accepted Answer

L.C.M = ( L.C.M . of 2, 4, 5, 7) / (H.C.F. of 3, 9, 6, 12) = 140/3

Question 16

L.C.M of 3/4, 6/7, 9/8 is?

Accepted Answer

L. C . M = ( L.C.M of 3, 6, 9 ) / (H.C.F of 4, 7, 8) = 18 / 1 = 18

Question 17

H.C.F . of 1/2, 3/4, 5/6, 7/8, 9/10 is?

Accepted Answer

H.C.F = ( H.C.F of 1, 3 , 5, 7, 9) / (L.C.M of 2, 4, 6, 8 , 10) = 1 / 120

Question 18

L.C.M of 3 3, 4, 4 2 and 3 is?

Accepted Answer

L.C.M of 33, 4, 42 and 3 = L.C.M of 33 x 24 = 27 x 16 = 432

Question 19

L.C.M of 87 and 145 is?

Accepted Answer

H.C.F of 87 and 145 is 29 ∴ L.C.M = ( 87 x 145) / 29 = 435

Question 20

Which of the following is a pair of co-primes?

Accepted Answer

H.C.F . of 18 and 25 is 1 So, 18 and 25 are co-primes

Problems on H.C.F and L.C.M Questions