Problems on H.C.F and L.C.M
- 1. About the number of pairs which have 16 as their H.C.F and 136 as their L.C.M. We can definitely say that?
Options- A. Only one such pair exists
- B. Only two such pair exists
- C. Many such pairs exists
- D. No such pair exists Discuss
Correct Answer: No such pair exists
Explanation:
H.C.F. of two numbers divides their L.C.M. exactly. Since 16 is not a factor of 136, it states that there does not exist any pair of numbers with H,C.F. 16 and L.C.M. 136.
- 2. The least number, which when divided by 16, 18 and 21 leaves the remainder 3, 5 and 8 respectively, is?
Options- A. 893
- B. 992
- C. 995
- D. 1024 Discuss
Correct Answer: 995
Explanation:
Here (16 - 3) = 13,
(18 - 5) = 13 and
(21 - 8 ) = 13
So, required number = (L . C . M of 16, 18, 21) - 13
= (1008 - 13)
= 995
- 3. The greatest number of four digits which is divisible by each one of the numbers 12, 18 21 and 28 is?
Options- A. 9848
- B. 9864
- C. 9828
- D. 9636 Discuss
Correct Answer: 9828
Explanation:
Required number is divisible by the L . C . M of 12, 18, 21, 28 i.e 252.
Now, greatest number of four digits = 9999
On dividing 9999 by 252, the remainder is 171
? Required number = (9999 - 171) = 9828.
- 4. The least number which when divided by 15, 27, 35 and 42, leaves in each case a remainder 7 is?
Options- A. 1883
- B. 1897
- C. 1987
- D. 2007 Discuss
Correct Answer: 1897
Explanation:
Required Number = (LCM of 15, 27, 35 and 42) + 7
= 1890 + 7
= 1897
- 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
Correct Answer: 9.60 m
Explanation:
Required length = L. C . M of (64, 80, 96) cm
= 960 cm
= 9.60 m.
- 6. 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
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.
- 7. 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
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 .
- 8. 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
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
- 9. 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
Correct Answer: 127
Explanation:
Required number = H.C.F of (1657 - 6) and (2037 - 5)
= H.C.F of 1651 and 2032
= 127
- 10. 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 Discuss
Correct Answer: 13
Explanation:
LCM 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
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