Problems on H.C.F and L.C.M
- 1. A person has completely put each of three liquids 403 L of petrol, 456 L of diesel and 496 L of mobile oil in in bottles of equal size without mixing any of the above three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?
Options- A. 34
- B. 44
- C. 46
- D. None of these Discuss
Correct Answer: 44
Explanation:
HCF of 403,456 and 496 = 31
Now, the number of bottles required to put 403 L of petrol = 403/31 = 13
Similarly,the number of bottles required to put 456 L of diesel = 465/31 = 15
The number of bottles required to put 496 L of mobile oil = 496/31 = 16
? Least number of bottles required having 31 L as capacity = 13+15 + 16 = 44
- 2. 30 pineapple trees, 45 orange tree and 60 mango trees have to be planted in rows such that each row contains the same number of trees of one variety only. What is minimum number number of row in which the trees may be planted?
Options- A. 10
- B. 15
- C. 25
- D. 9 Discuss
Correct Answer: 9
Explanation:
Minimum number of rows = Maximum number of trees in each row
= HCF of 30,45 and 60 = 15
? Number of rows = (30 + 45 + 60)/15 = 9
- 3. If HCF of x 3 - 10m 2 + 31x - 30m and x 2 - 8mx + 15 is a linear polynomial, then what is the value of m?
Options- A. 2
- B. 3
- C. 1
- D. 4 Also asked in: Bank Exams
Correct Answer: 1
Explanation:
Go through options.
Put m = 1 in two given expression,we have
x3 - 10x2 + 31x - 30 and x2 - 8x + 15
x2 - 8x + 15 = (x - 5) (x - 3)
x3 - 10x2 + 31x - 30 = (x - 2) (x - 5) (x - 3)
? (x - 5) (x - 3) = x2 - 8x + 15 is the HCF of both expressions.
? m = 1
- 4. What is the um of the digits of the least number which when divided by 54 leaves 35 as remainder, when divided by 80 leaves 61 as remainder and when divided by 119 leaves 100 leaves 100 as remainder?
Options- A. 21
- B. 19
- C. 23
- D. 28 Discuss
Correct Answer: 28
Explanation:
(54 - 35) = 19, (80 - 61) = 19 and(119 - 100) = 19
LCM of 54, 80 and 119 is 257040.
Required least number = 257040 + 19 = 257059
Sum of the digits of 257059 = 2 + 5 + 7 + 0 + 5 + 9 = 28
- 5. What is the sum of digits of the least number,which when divided by 52 leaves 33 as remainder, when divided by 78 leaves 59 as remainder and when divided by 117 leaves 98 as remainder?
Options- A. 21
- B. 27
- C. 19
- D. 36 Discuss
Correct Answer: 19
Explanation:
(52 - 33) = 19, (78 - 59) = 19 and (117 - 98) = 19
LCM of 52, 78 and 117 is 468.
Required least number = 468 + 19 = 487
Sum of digits of 487 = 4 + 8 + 7 = 19
- 6. The ratio of two numbers is 3 : 4 and their HCF is 4. What will be their LCM?
Options- A. 12
- B. 16
- C. 24
- D. 48 Discuss
Correct Answer: 48
Explanation:
According to the question,
1st number = 3M, 2nd number = 4M
where, M = HCF
But given, M = 4
We know that,
LCM = Product of two numbers / HCF
= (3M x 4M) / M
LCM = 12M = 12 x 4 = 48
- 7. The sum of two numbers is 1056 and their HCF is 66, Find the Number of such pairs.
Options- A. 6
- B. 2
- C. 4
- D. 8 Discuss
Correct Answer: 4
Explanation:
Let the numbers be 66a and 66b, where a and b are co-primes.
According to the question,
66a + 66b = 1056
? 66(a + b) = 1056
? (a + b) = 1056/66 = 16
? Possible values of a and b are
(a = 1, b = 15), (a = 3, b = 13).
(a = 5, b = 11 ), (a = 7, b = 9)
? Numbers are
(66 x 1, 66 x 15), (66 x 3, 66 x 13),
(66 x 5, 66 x 11), (66 x 7, 66 x 9).
? Possible number of pairs = 4
- 8. The HCF and LCM of two natural numbers are 12 and 72, respectively. What is the difference between the two numbers, if one of the number is 24?
Options- A. 12
- B. 18
- C. 21
- D. 24 Discuss
Correct Answer: 12
Explanation:
Second number = (LCM x HCF) / first number
= (72 x 12)/ 24 = 36
Difference between the two numbers
= 36 - 24 = 12
- 9. How many numbers are there between 4000 and 6000 which are exactly divisible by 32, 40, 48 and 60?
Options- A. 2
- B. 3
- C. 4
- D. 5 Discuss
Correct Answer: 4
Explanation:
LCM of 32, 40, 48 and 60 = 480
The number divisible by 480 between 4000 and 6000 are 4320, 4800, 5280 and 5760.
Hence, required number of numbers are 4.
- 10. For any integer n, What is HCF (22n + 7, 33n + 10) equal to?
Options- A. 0
- B. 1
- C. 11
- D. None of these Discuss
Correct Answer: 1
Explanation:
HCF of (22n + 7, 33n + 10) is always 1.
lllustraction
For n = 1, HCF(29, 43) ? HCF = 1
For n = 2, HCF(51, 76) ? HCF = 1
For n = 3, HCF(73, 109) ? HCF = 1
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