Problems on H.C.F and L.C.M
- 1. The smallest number, which when diminished by 3, is divisible by 21, 28, 36 and 45 is?
Options- A. 420
- B. 1257
- C. 1260
- D. 1263 Discuss
Correct Answer: 1263
Explanation:
Required number = (L . C . M of 21, 28, 36, 45 ) + 3
= (1260 + 3 )
= 1263
- 2. The number of prime factors in 2 222 x 3 333 x 5 555 is?
Options- A. 3
- B. 1107
- C. 1110
- D. 1272 Discuss
Correct Answer: 1110
Explanation:
The number of prime factors in the given product
= (222 + 333 + 555)
= 1110.
- 3. The H.C.F and L.C.M of two number are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is?
Options- A. 33
- B. 66
- C. 132
- D. 264 Discuss
Correct Answer: 132
Explanation:
First number = 2 x 44 = 88
Second number = (LCM x HCF ) / First number
? Second number = 44 x 264 / 88 = 132.
- 4. The LCM of two number is 48. The number are in the ratio of 2:3. Find sum of the numbers.
Options- A. 28
- B. 32
- C. 40
- D. 64 Discuss
Correct Answer: 40
Explanation:
Let the numbers be 2x and 3x.
So, their LCM = 6x
However, the LCM is given as 48
? 6x = 48
? x=8
So, the numbers are 16 and 24.
Hence, their sum is 40.
- 5. Find the greatest possible length which can be used to measure 4 m 3 cm, 4 m 34 cm and 4 m 65 cm exactly.
Options- A. 31 cm
- B. 29 cm
- C. 28 cm
- D. 32 cm Discuss
Correct Answer: 31 cm
Explanation:
Required measure = HCF of 403, 434 and 465 = 31 cm
- 6. Find the least number which when divided by 12, 15, 20 and 24 leaves the same remainder 2 in each case?
Options- A. 122
- B. 120
- C. 124
- D. 126 Discuss
Correct Answer: 122
Explanation:
Required number = LCM of (12, 15, 20, 24) + 2
= 120 + 2 = 122
- 7. If there number are 2a, 5a, and 7a, what will be their LCM?
Options- A. 70a
- B. 65a
- C. 75a
- D. 70a3 Discuss
Correct Answer: 70a
Explanation:
Required LCM = a x 2 x 5 x 7 = 70a
- 8. What will be the HCF of ( 2 x 3 x 7 x 9 ), ( 2 x 3 x 9 x 11 ) and ( 2 x 3 x 4 x 5 )?
Options- A. 2 x 3 x 7
- B. 2 x 3 x 9
- C. 2 x 3
- D. 2 x 7 x 9 x 11 Discuss
Correct Answer: 2 x 3
Explanation:
Given factors
2 x 3 x 7 x 9; 2 x 3 x 9 x 11; 2 x 3 x 4 x 5
? Required HCF = Product of common prime factors having least powers = 2 x 3
- 9. Find the LCM of 1/3, 2/9, 5/6 and 4/27.
Options- A. 1/54
- B. 10/27
- C. 20/3
- D. 3/20 Discuss
Correct Answer: 20/3
Explanation:
We known that,
LCM of fractions = (LCM of numerators) / (HCF of denominators)
? Required LCM = (LCM of 1, 2, 5, and 4) / (HCF of 3, 9, 6 and 27)
? = 20/3
- 10. Find the LCM of 2/3, 3/5, 4/7 and 9/13.
Options- A. 36
- B. 1/36
- C. 1/1365
- D. 12/455 Discuss
Correct Answer: 36
Explanation:
Required LCM = (LCM of 2, 3, 4, 9) / (HCF of 3, 5, 7, 13)
= (4 x 9)/1
= 36
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