Discussion
Home ‣ Aptitude ‣ Problems on H.C.F and L.C.M Comments
- Question
- Six bell commence tolling together and toll at intervals of 5, 10, 15, 20, and 30 s, respectively. In 60 min, how many times do they toll together?
Options- A. 20
- B. 15
- C. 13
- D. 11
- Correct Answer
- 13
ExplanationLCM of 5, 10, 15, 20, 25 and 30 is 300. So, the bell will toll together after every 300s (5min).
So, the number of times they toll together = 60/5 + 1=13 - 1. The greatest number by which if 1657 and 2037 are divided the remainders will be 6 and 5 respectively, is?
Options- A. 127
- B. 235
- C. 260
- D. 305 Discuss
- 2. The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder is?
Options- A. 1677
- B. 1683
- C. 2523
- D. 3363 Discuss
- 3. What least number must be subtracted from 1294 so that the remainder when divided by 9, 11, 13 will leave in each case the same remainder 6?
Options- A. 0
- B. 1
- C. 2
- D. 3 Discuss
- 4. The number of prime factors in the expression (6) 10 x (7) 17 x (11) 27 is?
Options- A. 54
- B. 64
- C. 71
- D. 81 Discuss
- 5. The measuring rods are 64 cm, 80 cm and 96 cm in length. The least length of cloth that can be measured exact number of times using any one of the above rods bis?
Options- A. 0.96 m
- B. 19.20 m
- C. 9.60 m
- D. 96.00 m Discuss
- 6. If the HCF of two positive integers is 26. Then their LCM cannot be?
Options- A. 78
- B. 104
- C. 144
- D. 234 Discuss
- 7. If the HCF of m and n is 1, then what are the HCF of m + n, m and HCF of m - n, n, respectively (where, m > n)?
Options- A. 2 and 1
- B. 1 and 1
- C. 1 and 2
- D. Cannot be determined Discuss
- 8. The LCM and HCF of two number are 240 and 16, respectively,If the two numbers are in the ratio 3 : 5, the numbers are?
Options- A. 24, 40
- B. 21, 35
- C. 36, 60
- D. 48, 80 Discuss
- 9. What are the values of c when the HCF of x 3 + c x 2 - x + 2c and x 2 + cx - 2 over the rational is a linear polynomial?
Options- A. +1
- B. +2
- C. +1
- D. +4 Discuss
- 10. What is the greatest number that divides 263, 935 and 1383 leaving a remainder of 7 in each case?
Options- A. 30
- B. 31
- C. 32
- D. 35 Discuss
Problems on H.C.F and L.C.M
Search Results
Correct Answer: 127
Explanation:
Required number = H.C.F of (1657 - 6) and (2037 - 5)
= H.C.F of 1651 and 2032
= 127
Correct Answer: 1683
Explanation:
L.C.M of 5, 6 , 7, 8 is 840
So, the number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2
? Required number = (840 x 2 + 3 ) = 1683
Correct Answer: 1
Explanation:
L. C .M of 9, 11, 13 is 1287
On dividing 1294 by 1287, the remainder is 7 .
? 1 must be subtracted from 1294, so that 1293 when divided by 9, 11, 13 leaves in each case the same remainder 6 .
Correct Answer: 64
Explanation:
Since 2, 3, 7, 11 are prime numbers and the given expression is
210 x 310 x 717 x 1127
So the number of prime factors in the given expression is (10 + 10 + 17 + 27 ) = 64.
Correct Answer: 9.60 m
Explanation:
Required length = L. C . M of (64, 80, 96) cm
= 960 cm
= 9.60 m.
Correct Answer: 144
Explanation:
LCM of the number is always divisible by the HCF of the same numbers.
So, 78, 104 and 234 are all divisible by 26. Whereas, 144 is not divisible by 26.
Thus, 144 cannot be the LCM of the number whose HCF is 26.
Correct Answer: 1 and 1
Explanation:
The HCF of m and n is 1, so m and n are prime number.
Let m = 7 and n = 5 ? m + n = 12
HCF of(m + n)and m = HCF of 12 and 7 = 1
Similarly, HCF of (m - n) and n = 1
Correct Answer: 48, 80
Explanation:
Suppose two numbers are 3N and 5N.
Then, 3N x 5N = HCF x LCM
? 15N2 = 16 x 240
? N2 = 256
? N = 16
So, the number are 3N = 3 x 16 = 48 and 5N = 5 x 16 = 80.
Correct Answer: +1
Explanation:
Find HCF of x3 +c x2 -x + 2c and x2 + cx - 2 by long division method and get remainder
? Remainder = 2c - 2/c
Since,remainder should be zero
? 2c2 - 2 = 0
? 2(c2 -1) = 0 ? c= ± 1
Correct Answer: 32
Explanation:
The required greatest number is the HCF of (263 - 7, 935 - 7, 1383 - 7)
i.e., HCF of 256, 928 and 1376 = 32
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