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Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:
- a)58 and 13 or 16 and 29
- b)68 and 23 or 36 and 49
- c)18 and 73 or 56 and 93
- d)78 and 13 or 26 and 39
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Pairs of natural numbers whose least common multiple is 78 and the gre...
Let the no.s be a & b,
GCD [ a , b ] = 13;
=> Let a = 13m and b = 13n
Now, LCM [ a , b ] = 78
=> 13m | 78
=> m | 6 and similarly, n | 6; --> Also, m does not divide n
.'. Possible values of (m,n) are :->
--> [ 1 , 6 ] , [ 2 , 3 ]
.'. Possible values for ( a , b ) are :-> [ 13 , 78 ] , [ 26 , 39 ]
Most Upvoted Answer
Pairs of natural numbers whose least common multiple is 78 and the gre...
Solution:
Given, LCM = 78 and GCD = 13
Let the required pair of numbers be a and b.
Therefore, a × b = LCM × GCD
=> a × b = 78 × 13
=> a × b = 1014
Now, we need to find the pair of natural numbers whose product is 1014.
Prime factorizing 1014, we get:
1014 = 2 × 3 × 13 × 13
Hence, the only possible pairs of natural numbers whose product is 1014 are:
(2, 507), (3, 338), (6, 169), (13, 78), (18, 57), (26, 39)
Out of these pairs, we need to find the pair whose GCD is 13.
Let's check each pair:
- (2, 507) => GCD = 1
- (3, 338) => GCD = 1
- (6, 169) => GCD = 1
- (13, 78) => GCD = 13
- (18, 57) => GCD = 3
- (26, 39) => GCD = 13
Hence, the possible pairs of natural numbers whose LCM is 78 and GCD is 13 are (13, 78) and (26, 39).
Therefore, the correct answer is option 'D': 78 and 13 or 26 and 39.
Given, LCM = 78 and GCD = 13
Let the required pair of numbers be a and b.
Therefore, a × b = LCM × GCD
=> a × b = 78 × 13
=> a × b = 1014
Now, we need to find the pair of natural numbers whose product is 1014.
Prime factorizing 1014, we get:
1014 = 2 × 3 × 13 × 13
Hence, the only possible pairs of natural numbers whose product is 1014 are:
(2, 507), (3, 338), (6, 169), (13, 78), (18, 57), (26, 39)
Out of these pairs, we need to find the pair whose GCD is 13.
Let's check each pair:
- (2, 507) => GCD = 1
- (3, 338) => GCD = 1
- (6, 169) => GCD = 1
- (13, 78) => GCD = 13
- (18, 57) => GCD = 3
- (26, 39) => GCD = 13
Hence, the possible pairs of natural numbers whose LCM is 78 and GCD is 13 are (13, 78) and (26, 39).
Therefore, the correct answer is option 'D': 78 and 13 or 26 and 39.
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D
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Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer?
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Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer?.
Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer?.
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Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:a)58 and 13 or 16 and 29b)68 and 23 or 36 and 49c)18 and 73 or 56 and 93d)78 and 13 or 26 and 39Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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