Problems on H.C.F and L.C.M
- 1. The H.C.F. of 9⁄10, 12⁄25, 18⁄35 and 21⁄40 is:
Options- A. 3⁄5
- B. 252⁄5
- C. 3⁄1400
- D. 63⁄700 Discuss
Correct Answer: 3⁄1400
Explanation:
| Required H.C.F. = | H.C.F. of 9, 12, 18, 21 | = | 3 |
| L.C.M. of 10, 25, 35, 40 | 1400 |
- 2. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Options- A. 4
- B. 7
- C. 9
- D. 13 Discuss
Correct Answer: 4
Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
- 3. 252 can be expressed as a product of primes as:
Options- A. 2 x 2 x 3 x 3 x 7
- B. 2 x 2 x 2 x 3 x 7
- C. 3 x 3 x 3 x 3 x 7
- D. 2 x 3 x 3 x 3 x 7 Discuss
Correct Answer: 2 x 2 x 3 x 3 x 7
Explanation:
Clearly, 252 = 2 x 2 x 3 x 3 x 7
- 4. The G.C.D. of 1.08, 0.36 and 0.9 is:
Options- A. 0.03
- B. 0.9
- C. 0.18
- D. 0.108 Discuss
Correct Answer: 0.18
Explanation:
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.
- 5. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Options- A. 9000
- B. 9400
- C. 9600
- D. 9800 Discuss
Correct Answer: 9600
Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
∴ Required number (9999 - 399) = 9600.
- 6. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
Options- A. 15 cm
- B. 25 cm
- C. 35 cm
- D. 42 cm Discuss
Correct Answer: 35 cm
Explanation:
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.
- 7. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
Options- A. 28
- B. 32
- C. 40
- D. 64 Discuss
Correct Answer: 40
Explanation:
Let the numbers be 2 x and 3 x
Then, their L.C.M. = 6x.
So, 6x = 48 or x = 8.
∴ The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40.
- 8. Find the highest common factor of 36 and 84.
Options- A. 4
- B. 6
- C. 12
- D. 18 Discuss
Correct Answer: 12
Explanation:
36 = 2 2 x 3 2
84 = 22 x 3 x 7
∴ H.C.F. = 22 x 3 = 12.
- 9. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
Options- A. 3
- B. 13
- C. 23
- D. 33 Discuss
Correct Answer: 23
Explanation:
L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
∴ Number to be added = (60 - 37) = 23.
- 10. The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
Options- A. 12
- B. 16
- C. 24
- D. 48 Discuss
Correct Answer: 48
Explanation:
Let the numbers be 3 x and 4 x . Then, their H.C.F. = x . So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
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