LCM and HCF: Solved 50 LCM and HCF Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

LCM and HCF Questions

1. Find the least number which when divided by 12, 27 and 35 leaves 6 as a remainder?




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Correct Ans:3786
Explanation:
Find the least number which when divided by 12, 27 and 35 leaves 6 as a remainder:

Let find the answer:

Number = LCM (12, 17, 35) + 6
= 3780 + 6
= 3786


2. Find the 4-digit smallest number which when divided by 12, 15, 25, 30 leaves no remainder?




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Correct Ans:1200
Explanation:
Find the 4-digit smallest number which when divided by 12, 15, 25, 30 leaves no remainder:

Explanation :

LCM of 12, 15, 25 and 30 is 300

least number of 4-digit divided by 300 is 1200


3. Find the least number which when divided by 2, 3, 4 and 5 leaves a remainder 3. But when divided by 9 leaves no remainder?




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Correct Ans:63
Explanation:
Find the least number which when divided by 2, 3, 4 and 5 leaves a remainder 3. But when divided by 9 leaves no remainder:

Explanation :

LCM of 2, 3, 4 and 5 is 30,
let number be 30k + 3 put k = 2,

we get 63 which is divisible by 9


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4. Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?




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Correct Ans:36
Explanation:
Since each iron rod must be cut into parts of equal length and each part must be as long as possible, so HCF should be taken.
HCF of 78, 104, 117, 169 = 13
Number of pieces from 78 cm rod = 78/13 = 6
Number of pieces from 104 cm rod = 104/13 = 8
Number of pieces from 117 cm rod = 117/13 = 9
Number of pieces from 78 cm rod = 169/13 = 13
Total number of pieces = 6 + 8 + 9 + 13 = 36.


5. Find the greatest number which when divides 564 and 467 leaves the remainder as 4 and 7 respectively.




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Correct Ans:20
Explanation:
The greatest number which when divides 564 and 467 leaves the remainder as 4 and 7.
564 - 4 = 560
467 - 7 = 460
HCF (560, 460) = 20
So, the greatest number is 20.


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6. The product of LCM and HCF of two numbers is 48. The difference of two numbers is 8. Find the numbers?




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Correct Ans:4, 12
Explanation:
Let the numbers be 'a' and 'b'.
WKT, Product of two numbers = LCM × HCF
Product of two numbers = 48
ab = 48
Difference of two numbers = 8
a - b = 8
Factors of ab are (1,48) , (2,24), (3,16),(4,12),(6,8).
Here, the only pair which satisfies the given condition is (4, 12).


7. Four different electronic devices make a beep after every 30 minutes, 1 hour, 1 hour 30 minutes and 1 hour 45 minutes respectively. All the device beeped together at 12 noon. They will again beep together at




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Correct Ans:9:00 AM
Explanation:
Interval after the devices will beep together = (L.C.M. of 30, 60, 90, 105) min
= 1260 min
= 1260/60 = 21 hrs
So, the devices will again beep together after 21 hrs i.e., at 9 AM(after 12 noon).


8. What is the LCM of (6x³ + 60x² + 150x) and (3x⁴ + 12x³ – 15x²)?




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Correct Ans:6x2(x + 5)2(x – 1)
Explanation:
First polynomial = 6x³ + 60x² + 150x
= 6x (x² + 10x + 25)
= 3 × 2 × x × (x + 5)²
Second polynomial = 3x⁴ + 12x³ – 15x²
= 3x² (x² + 4x – 5)
= 3x² (x² + 5x – x – 5)
= 3x² (x + 5) (x – 1)

Required LCM = 3 × 2 × x² × (x + 5)² (x – 1)
= 6x² (x + 5)² (x – 1)


9. On dividing a number by 4, the remainder is 2. The quotient so obtained when divided by 5, leaves the remainder 3. Now the quotient so obtained when divided by 6, leaves the remainder 5. The last quotient is 7. The number was




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Correct Ans:954
Explanation:


WKT,
Divisor x Quotient + Remainder = Number
6 x 7 + 5 = 47
5 x 47 + 3 = 238
4 x 238 + 2 = 954
Therefore, required number is 954.


10. The HCF and LCM of two numbers are 8 and 48 respectively. If one of the numbers is24, then the other number is




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Correct Ans:16
Explanation:
First number * Second number = HCF * LCM
24 * Second number = 8 *48
Second number = (8 * 48)/24 = 16


11. HCF of 2/3, 4/5 and 6/7 is




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Correct Ans:2/105
Explanation:
Given fractions = 2/3, 4/5 and 6/7
HCF of fractions = HCF of numerators / LCM of denominators
= HCF (2, 4, 6) / LCM (3, 5, 7)
= 2/105


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12. What is the LCM of 120 and 450?




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Correct Ans:1800
Explanation:
LCM of 120 = 2, 2, 2, 3
LCM of 450 = 2, 3, 3, 5, 5
LCM of 120 and 450 = 2 * 2 * 2 * 3 * 3 * 5 * 5
= 1800


13. HCF of x2 - y2 and x3 - y3 is




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Correct Ans:x - y
Explanation:
x2 - y2 = (x + y) (x - y)
x3 - y3 = (x - y) (x2 + xy + y2)
HCF = (x - y)


14. The HCF of two numbers is 24. The number which can be their LCM is




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Correct Ans:120
Explanation:
HCF always divides LCM completely.
By option LCM is 120.


15. The sum of two number is 528 and their HCF is 33. How many pairs of such numbers can be?




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Correct Ans:4
Explanation:
Here, the HCF = 33
Then, let the two numbers be 33a and 33b,
Respectively, where a and b are coprime.
Then, 33a + 33b = 528
a + b = 16
Hence, values of (a, b) which are coprime to each other can be
(1, 15), (3, 13), (5, 11) and (7, 9).
Hence, required number of pairs is 4.


16. Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of the two number is




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Correct Ans:60
Explanation:
Let the numbers be 3x and 4x.
LCM of 3x and 4x = 12x
Given, LCM = 240
12x = 240
x = 240/12 = 20
Smaller number = 3x = 3 * 20 = 60


17. The length, breadth and height of a room are 363m, 528m and 693m respectively. Determine the longest tape that can measure the three dimensions of the room exactly.




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Correct Ans:33 metre
Explanation:
Maximum length of tape
= HCF of 363m, 528m and 693m
363 = 3 * 11 * 11
528 = 2 * 2 * 2 * 2 * 3 * 11
693 = 3 * 3 * 7 * 11
HCF of 363m, 528m and 693m = 3 * 11
= 33 metre


18. The product of two numbers is 35828 and their HCF is 26. Find their LCM.




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Correct Ans:1378
Explanation:
Required LCM = Product of numbers/Their HCF
= 35828/26 = 1378


19. Find the highest common factor of 72 and 168.




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Correct Ans:24
Explanation:
HCF of 72 and 168,
72 => 2 * 2 * 2 * 3 * 3
168 => 2 * 2 * 2 * 3 * 7
Thersfore, HCF = 2 * 2 * 2 * 3 = 24


20. The HCF of 252, 294 and 3#8 is 42, what is #?




SHOW ANSWER
Correct Ans:7
Explanation:
Multiples of 42
= 252, 294, 336, 378
So, # = 7





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