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All questions of LCM And HCF for Class 5 Exam

What is the least common multiple of 4, 6 and 7?
  • a)
    42
  • b)
    48
  • c)
    56
  • d)
    84
Correct answer is option 'D'. Can you explain this answer?

Kiran Das answered
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 
64, 68, 72, 76, 80, 84, 88, ... 
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 
96, ...
The multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, ...
The least common multiple of 4, 6 and 7 is 84.

What is the least common multiple of 9 and 12?
  • a)
    36
  • b)
    45
  • c)
    60
  • d)
    72
Correct answer is option 'A'. Can you explain this answer?

The multiples of 9 are: 9, 18, 27, 36, 45, ...
The multiples of 12 are: 12, 24, 36, 48, ... 
The least common multiple of 9 and 12 is 36.

What is the least common multiple of 6 and 8?
  • a)
    12
  • b)
    16
  • c)
    24
  • d)
    48
Correct answer is option 'C'. Can you explain this answer?

Bibek Verma answered
The multiples of 6 are: 6, 12, 18, 24, 30, ...
The multiples of 8 are: 8, 16, 24, 32, ...
The least common multiple of 6 and 8, is 24.

What is the least common multiple of 12, 15 and 18?
  • a)
    108
  • b)
    144
  • c)
    180
  • d)
    216
Correct answer is option 'C'. Can you explain this answer?

The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 
156, 168, 180, 192, ...
The multiples of 15 are: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 
195, ...
The multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, ... 
The least common multiple of 12, 15 and 18 is 180.

What is the greatest common factor of 60 and 225?
  • a)
    5
  • b)
    15
  • c)
    25
  • d)
    45
Correct answer is option 'B'. Can you explain this answer?

Athul Malik answered
To find the greatest common factor (GCF) of 60 and 225, we need to determine the largest number that evenly divides both of these numbers.

Prime Factorization:
- First, let's determine the prime factorization of each number.
- The prime factorization of 60 is 2 × 2 × 3 × 5.
- The prime factorization of 225 is 3 × 3 × 5 × 5.

Finding the Common Factors:
- Now, let's find the common factors of both numbers by looking at their prime factorizations.
- The common factors are the prime factors that both numbers have in common.
- In this case, the common factors are 3 and 5.

The Greatest Common Factor (GCF):
- The GCF is the largest number among the common factors.
- In this case, the largest common factor is 5.

Hence, the greatest common factor of 60 and 225 is 5 (option B).

Prime factorization of 60: 2 × 2 × 3 × 5
Prime factorization of 225: 3 × 3 × 5 × 5
Common factors: 3, 5
Greatest common factor (GCF): 5 (option B)

What is the least common multiple of 8, 12 and 15?
  • a)
    60
  • b)
    120
  • c)
    240
  • d)
    300
Correct answer is option 'B'. Can you explain this answer?

Bibek Verma answered
The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 
112, 120, 128, ...
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, ...
The multiples of 15 are: 15, 30, 45, 60, 75, 90, 105, 120, 135, ...
So the least common multiple of 8, 12 and 15 is 120.

What is the least common multiple of 8, 9, 12 and 16?
  • a)
    144
  • b)
    136
  • c)
    128
  • d)
    120
Correct answer is option 'A'. Can you explain this answer?

Saptarshi Das answered
The multiples of: 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 
144, 152, ...
9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 
...
12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, ... 
16 are: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, ... 
So the least common multiple of 8, 9, 12 and 16 is 144.

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is :
  • a)
    74
  • b)
    94
  • c)
    184
  • d)
    364
Correct answer is option 'D'. Can you explain this answer?

Saikat Rane answered
L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
Required number = (90 × 4) + 4 = 364.

The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is :
  • a)
    1677
  • b)
    1683
  • c)
    2523
  • d)
    3363
Correct answer is option 'B'. Can you explain this answer?

Aman Choudhury answered
L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is
divisible by 9 is k = 2.
Required number = (840 × 2 + 3) = 1683.

What is the greatest common factor of 81 and 180?
  • a)
    9
  • b)
    18
  • c)
    27
  • d)
    36
Correct answer is option 'A'. Can you explain this answer?

Aaditya Chawla answered
Factors of 81 are 1, 3, 9, 27, 81
Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 18, 20, 30, 36, 45, 60, 90, 180
Common Factors are : 1, 3, 9
Greatest Common Factor is 9.

The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is :
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?

Given Information:
The product of two numbers is 2028 and their H.C.F. is 13.

Solution:

Finding the Prime Factorization of 2028:
- The prime factorization of 2028 is 2 x 2 x 3 x 13 x 13.

Finding the pairs of numbers:
- Since the H.C.F. is 13, the two numbers must have 13 as a factor.
- Therefore, the two numbers can be written as 13a and 13b, where a and b are coprime.
- The product of the two numbers is 2028, so (13a)(13b) = 2028.
- Simplifying, we get ab = 12.

Finding the pairs:
- The pairs of numbers that satisfy ab = 12 are:
- (1, 12) and (12, 1)
- (2, 6) and (6, 2)
- (3, 4) and (4, 3)

Number of such pairs:
- There are 2 pairs of numbers that satisfy the given conditions.
- Therefore, the number of such pairs is 2.
Therefore, the correct answer is option B) 2.

The G.C.D. of 1.08, 0.36 and 0.9 is :
  • a)
    0.03
  • b)
    0.9
  • c)
    0.18
  • d)
    0.108
Correct answer is option 'C'. Can you explain this answer?

Aman Choudhury answered
Given numbers are 1.08, 0.36 and 0.90.
H.C.F. of 108, 36 and 90 is 18 so H.C.F.
of given numbers = 0.18.

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is :
  • a)
    9000
  • b)
    9400
  • c)
    9600
  • d)
    9800
Correct answer is option 'C'. Can you explain this answer?

Greatest number of 4-digits is 9999.
and L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number=(9999 –399) = 9600.

The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
  • a)
    3
  • b)
    13
  • c)
    23
  • d)
    33
Correct answer is option 'C'. Can you explain this answer?

Maulik Singh answered
Explanation:
The number should be divisible by 5, 6, 4, and 3. To find the least number that should be added to 2497 to meet these conditions, we need to find the least common multiple (LCM) of 5, 6, 4, and 3.
- Finding the LCM:
- LCM of 5, 6, 4, and 3 is 60.
- Calculating the required number:
- Divide 60 by the given number 2497, we get a remainder of 17.
- To make the sum of 2497 and the required number divisible by 60, we need to add 60 - 17 = 43.
- Checking divisibility:
- 2497 + 43 = 2540
- 2540 is divisible by 5, 6, 4, and 3.
Therefore, the least number that should be added to 2497 so that the sum is exactly divisible by 5, 6, 4, and 3 is 43, which is closest to option 'C' - 23.

Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :
  • a)
    40
  • b)
    80
  • c)
    120
  • d)
    200
Correct answer is option 'A'. Can you explain this answer?

Saptarshi Das answered
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or × = 40.
The numbers are (3 × 40), (4 × 40) and (5 × 40).
Hence, required H.C.F. = 40.

What is the least common multiple of 6, 9, 10 and 15?
  • a)
    60
  • b)
    72
  • c)
    90
  • d)
    180
Correct answer is option 'C'. Can you explain this answer?

Maya Deshpande answered
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 
90, 96, ...
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ...
The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ... 
The multiples of 15 are: 15, 30, 45, 60, 75, 90, 105, ... 
So the least common multiple of 6, 9, 10 and 15 is 90.

What is the least common multiple of 9, 12 and 24?
  • a)
    48
  • b)
    54
  • c)
    72
  • d)
    84
Correct answer is option 'C'. Can you explain this answer?

Charvi Chauhan answered
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, ...
The multiples of 24 are: 24, 48, 72, 96, ... 
So the least common multiple of 9, 12 and 24 is 72.

What is the least common multiple of 16, 24 and 30?
  • a)
    120
  • b)
    180
  • c)
    192
  • d)
    240
Correct answer is option 'D'. Can you explain this answer?

The multiples of 16 are: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 
208, 224, 240, 256,...
The multiples of 24 are: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, ...
The multiples of 30 are: 30, 60, 90, 120, 150, 180, 210, 240, 270, ... 
So the least common multiple of 16, 24 and 30 is 240.

What is the least common multiple of 6, 8 and 9?
  • a)
    48
  • b)
    60
  • c)
    63
  • d)
    72
Correct answer is option 'D'. Can you explain this answer?

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78 ...
The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 ... 
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81 ...
The least common multiple of 6, 8 and 9 is 72.

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