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Home ‣ Aptitude ‣ Problems on H.C.F and L.C.M Comments
- Question
- The product of two-digit numbers is 2160 and their G.C.M is 12. The numbers are?
Options- A. 72, 30
- B. 36, 60
- C. 96, 25
- D. None of these
- Correct Answer
- 36, 60
ExplanationLet the number be 12a and 12b
Then 12a x 12b = 2160
or ab = 15
? Values of co-primes a and b are (1, 15), (3, 5)
So, the two digit number are 12 x 3 and 12 x 5 i.e. 36 and 60 . - 1. The sum of two number is 216 and their H.C.F is 27. The numbers are?
Options- A. 54, 162
- B. 108, 108
- C. 27, 189
- D. None of these Discuss
- 2. The greatest possible length which can be used to measure exactly the lengths 7m, 3m 85cm, 12m 95 cm, is?
Options- A. 15 cm
- B. 25 cm
- C. 35 cm
- D. 42 cm Discuss
- 3. An inspector of schools wishes to distribute 84 balls and 180 bats equally among a number of boys. Find the greatest number receiving the gift in this ways?
Options- A. 14
- B. 15
- C. 16
- D. 12 Discuss
- 4. What least number must be subtracted from 1936, so that the remainder when divided by 9, 10, 15 will leave in each case the same remainder 7?
Options- A. 46
- B. 53
- C. 39
- D. 44 Discuss
- 5. Find the sum of three numbers which are prime to one another such that the product of the first two is 437 and that of the last two is 551?
Options- A. 91
- B. 81
- C. 71
- D. 70 Discuss
- 6. The H.C.F of two number is 16 and their L.CM is 160. If one of the numbers is 32, then the other number is?
Options- A. 48
- B. 80
- C. 96
- D. 112 Discuss
- 7. The product of two numbers is 1600 and their H.C.F is 5. The L.C.M. of the numbers is?
Options- A. 320
- B. 1605
- C. 1595
- D. 8000 Discuss
- 8. 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
- 9. 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
- 10. 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
Problems on H.C.F and L.C.M
Search Results
Correct Answer: 27, 189
Explanation:
Let the number be 27a and 27b
Then, 27a + 27b = 216
or a + b = 216/27 = 8
? Values of co-primes with sum 8 are (1, 7) and (3, 5)
So, the number are (27 x 1 , 27 x 7) i.e. (27, 189)
Correct Answer: 35 cm
Explanation:
Required length = H.C.F of 700, 385, 1295 cm
= 35 cm.
Correct Answer: 12
Explanation:
Find the H.C.F. of 84 and 180, which is 12 and this is the required answer .
Correct Answer: 39
Explanation:
The L.C.M of 9, 10, 15 = 90
On dividing 1936 by 90, the remainder = 46
But a part of this remainder = 7
Hence, the two numbers = 46 - 7 = 39.
Correct Answer: 71
Explanation:
From the question we see that the second number is a common factor of the two products and since the numbers are prime to one another. It is their . H. C. F . and is, therefore, 19.
? The first number = 437 / 19 = 23
and the third number = 551 / 19 = 29
Hence, the number are 23, 19 and 29
? Sum = 23 + 19 + 29
= 71.
Correct Answer: 80
Explanation:
Product of two numbers = LCM of two numbers x HCF of two numbers.
? N x 32 = 160 x 16
? N = 80
Correct Answer: 320
Explanation:
Product of two numbers = LCM of two numbers x HCF of two numbers.
? 1600 = LCM x 5
? LCM = 320
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.
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
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.
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