Practice MCQ Questions and Answer on Problems on H.C.F and L.C.M

21.

Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:

• (A) 40
• (B) 80
• (C) 120
• (D) 200

Show Answer

 Let the numbers be 3x, 4x and 5x Then, their L.C.M. = 60x So, 60x = 2400 or x = 40 ∴ The numbers are (3 x 40), (4 x 40) and (5 x 40) Hence, required H.C.F. = 40

22.

A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7, is = ?

• (A) 1539
• (B) 539
• (C) 359
• (D) 1359

Show Answer

 10 - 9 = 1 9 - 8 = 1 8 - 7 = 1 ∴ LCM of (10, 9, 8) = 5 × 2 × 9 × 4 = 360 ∴ Required result = 360 - 1 = 359

23.

The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

• (A) 1008
• (B) 1015
• (C) 1022
• (D) 1032

Show Answer

 Required number = (L.C.M. of 12,16, 18, 21, 28) + 7    = 1008 + 7    = 1015

24.

The HCF of two numbers is 29, and the other factors of their LCM are 15 and 13. The larger of the two numbers is:

• (A) 435
• (B) 377
• (C) 406
• (D) 464

Show Answer

 Let the numbers are a and b HCF = 29 LCM = HCF (a × b) LCM = 29(15 × 13) Largest number = 15 × 29 = 435

25.

The HCF and LCM of two numbers are 12 and 336 respectively. If one of the numbers is 84, the other is = ?

• (A) 36
• (B) 48
• (C) 72
• (D) 96

Show Answer

 $$\eqalign{ & {\text{Other number}} \cr & {\text{= }}\left( {\frac{{12 \times 336}}{{84}}} \right)\cr & = 48 \cr} $$

26.

If the product of three consecutive numbers is 210, then the sum of the smaller numbers is = ?

• (A) 3
• (B) 4
• (C) 5
• (D) 11

Show Answer

 210 = 21 × 10 = 7 × 3 × 2 × 5 take 2 and 3 with together then we find number is 5, 6, 7 which is consecutive number so, 1st + 2nd = 5 + 6 = 11

27.

The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of four numbers

• (A) 17
• (B) 14
• (C) 21
• (D) 24

Show Answer

 x, x + 1, x + 2, x + 3 1st + 2nd = 4th x + x + 1 = x + 3 x = 2 2, 3, 4, 5 = 2 + 3 + 4 + 5 = 14

28.

The least number of square tiles required to pave the ceiling of a room 15m 17cm long and 9m 2cm broad is = ?

• (A) 656
• (B) 738
• (C) 814
• (D) 902

Show Answer

 For the least number of tiles, the size of the tiles must be the maximum. Maximum size of the tile = HCF of 1517 cm and 902 cm = 41 cm. Hence, required number of tiles $$\eqalign{ & {\text{ = }}\frac{{{\text{Area of ceiling}}}}{{{\text{Area of each tile}}}} \cr & = \left( {\frac{{1517 \times 902}}{{41 \times 41}}} \right) \cr & = 814 \cr} $$

29.

If r is the remainder when each of 7654, 8506, and 9997 is divided by the greatest number d (d > 1) then d - r is equal to = ?

• (A) 14
• (B) 18
• (C) 24
• (D) 28

Show Answer

 d = HCF of (8506 - 7654), (9997 - 8506), (9997 - 7654) = HCF of 852, 1491, 2343 = 213 $$\eqalign{ & {\text{213}}\overline {){\text{ 7654 (}}} 35 \cr & \,\,\,\,\,\,\,\,\,\,\frac{{639}}{{{\text{ }}1264}} \cr & \,\,\,\,\,\,\,\,\,\,\frac{{{\text{ }}1065}}{{{\text{ }}199}} \cr & {\text{Clearly r = 199}} \cr & \therefore d - r = 213 - 199 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 14 \cr} $$

30.

The G.C.D. of 1.08, 0.36 and 0.9 is:

• (A) 0.03
• (B) 0.9
• (C) 0.18
• (D) 0.108

Show Answer

 Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, ∴ H.C.F. of given numbers = 0.18