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Home ‣ Aptitude ‣ Problems on H.C.F and L.C.M Comments
- Question
- 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
- Correct Answer
- 44
ExplanationHCF 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 - 1. A, B, and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252s, B in 308s and C in 198s, all starting of the same point. After what time will they meet again at the string point?
Options- A. 26 min and 18s
- B. 42 min and 36s
- C. 45 min
- D. 46 min and 12s Discuss
- 2. A man has four copper rods whose lengths are 52 m, 65 m, 78 m, 91 m, respectively. This man wants to cut pieces of same length from each of four rods. what is the least number of total pieces if he is to cut without any wastage?
Options- A. 23
- B. 24
- C. 22
- D. 20 Discuss
- 3. What is the LCM of (x 2 - y 2 - z 2 - 2yz), (x 2 - y 2 + z 2 + 2xz) and (x 2 + y 2 - z 2 - 2xy)?
Options- A. (x + y + z) (x + y - z) (x - y + z)
- B. (x + y + z) (x - y - z) (x - y + z)
- C. (x + y + z) (x + y - z) (x - y - z)
- D. (x + y - z) (x - y - z) (x - y + z) Discuss
- 4. A, B and C start at the same time in the same direction to run around in 252s, B in 308s and C in 198s, all starting at the same point. After what time will they meet again at the starting point?
Options- A. 26 min and 18s
- B. 42 min and 36s
- C. 45 min
- D. 46 min and 12s Discuss
- 5. There are five hobby clubs in a college viz. photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meets on the same day within 180 days?
Options- A. 3
- B. 5
- C. 10
- D. 18 Discuss
- 6. 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
- 7. 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 Discuss
- 8. 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
- 9. 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
- 10. 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
Problems on H.C.F and L.C.M
Search Results
Correct Answer: 46 min and 12s
Explanation:
The time which all the three persons meet will be the LCM of the time by each person individually to complete one round.
252 = 22 x 71 x 91
308 = 22 x 71 x 111
198 = 21 x 91 x 111
? LCM of 252, 308 and 198 = 22 x 71 x 91 x 111 = 2772
So,A,B and C will again meet at the starting point in 2772 i.e.,46 min and 12s.
Correct Answer: 22
Explanation:
The pieces cut from four rods is least, so length of the pieces is the HCF of 52, 65, 78 and 91 which is 13.
? Number of pieces cut =(52 + 65 + 78 + 91)/13 = 22
Correct Answer: (x + y + z) (x - y - z) (x - y + z)
Explanation:
x2 - y2 - z2 - 2yz = x2 - (y + z)2 = (x+ y + z)(x - y - z)
x2 - y2 + z2 + 2yz = (x + z)2 - y2 = (x + y + z) (x + y - z)
x2 + y2 - z2 - 2xy = (x - y)2 - z2 = (x - y + z) (x - y - z)
? LCM = (x + y + z) (x - y - z) (x - y + z)
Correct Answer: 46 min and 12s
Explanation:
The time at which all the three persons meet will be the LCM of the time taken by each person individually to complete one round.
252 = 22 x 71 x 91
308 = 22 x 71 x 111
198 = 21 x 91 x 111
? LCM of 252, 308 and 198 = 22 x 71 x 91 x 111 = 2772
So, A, B and C will again meet at the starting point in 2772s i.e., 46 min and 12s
Correct Answer: 3
Explanation:
Gardening group meets once in 2 days, electronics group meets once in 3 days, chess group meets once in 4 days, yachting group meets once in 5 days and the photography group meets once in 6 days.
If they meet on the same day at one time, then the next time they will meet on same day again will be the LCM of 2, 3, 4, 5 and 6 which is equal to 60.
Hence, within 180 days all the five groups will meet on the same day = 180/60 = 3 times.
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
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
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
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
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
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