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Home ‣ Aptitude ‣ Problems on H.C.F and L.C.M Comments
- Question
- Find the number lying between 900 and 1000 which when divided by 38 and 57, leaves in each case a remainder 23?
Options- A. 935
- B. 945
- C. 925
- D. 955
- Correct Answer
- 935
ExplanationThe least common multiple of 38 and 57 is 114 and the multiple which is between 900 and 1000 is 912.
Now, 912 + 23 i,e 935 lies between 900 and 1000 and when divided by 38 and 57 leaves in each case 23 as the remainder.
Therefore, 935 is number required. - 1. 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
- 2. The least number which when divided by 12,16 and 18 leaves 5 as remainder in each case. Find the number.
Options- A. 139
- B. 144
- C. 149
- D. 154 Discuss
- 3. 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
- 4. The Product of two whole numbers is 1500 and their HCF is 10, Find the LCM.
Options- A. 15000
- B. 150
- C. 1500
- D. 15 Discuss
- 5. The LCM of two numbers is 48. The numbers are in the ratio of 2 : 3. Find the sum of the numbers.
Options- A. 28
- B. 32
- C. 40
- D. 64 Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Problems on H.C.F and L.C.M
Search Results
Correct Answer: 1
Explanation:
The number when divided by 9, 11, 13 leaving remainder 6 = (i.c.m. of 9, 11, 13) + 6 = 1293
Required least number = 1294 - 1293 = 1.
Correct Answer: 149
Explanation:
Given, a = 12, b =16 , c =18, k = 5
According to the formula,
Required number =(LCM of a, b and c) + k
= (LCM Of 12, 16, 18) + 5
LCM of 12, 16, 18 is
? LCM = 2 x 2 x 3 x 4 x 3 = 144
? Required number =144 + 5 = 149
Correct Answer: 23
Explanation:
LCM of 5, 6, 4 and 3 = 60
On dividing 2497 by 60, the remainder is 37.
? Number to be added = 60 - 37 = 23
Correct Answer: 150
Explanation:
Given that, product of two numbers =1500
HCF = 10
According to the formula,
Product of two numbers = HCF x LCM
? 1500 = 10 x LCM
? LCM = 1500/10 =150
Correct Answer: 40
Explanation:
Let numbers are 2N and 3N.
According to the question, 6N = 48
? N = 8 ( ? LCM = 6N )
? Required sum = ( 2N + 3N ) = 5N
= 5 x 8 = 40
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: 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: 12
Explanation:
Find the H.C.F. of 84 and 180, which is 12 and this is the required answer .
Correct Answer: 35 cm
Explanation:
Required length = H.C.F of 700, 385, 1295 cm
= 35 cm.
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)
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