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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?
Verified Answer
Pairs of natural numbers whose least common multiple is 78 and the gre...
Given- least common factor (LCM) = 78
 Greatest divisor is also a HCF = 13
As, we know ,    HCF x LCM = A x B ( A and B are two natural no. of which LCM and HCF is given)
Therefore, req product of no. = 13 x 78 = A x B =1014 or 2*3*13*13
since 13 is common in both no. as its hcf is 13
req no.= 13*3=39 and 13*2 = 26 
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Pairs of natural numbers whose least common multiple is 78 and the gre...
Solution:
We are given that:
LCM (Least Common Multiple) = 78
GCD (Greatest Common Divisor) = 13

Let's find the prime factorization of 78 to identify the possible pairs of natural numbers:
78 = 2 x 3 x 13

Possible pairs of natural numbers with LCM = 78 and GCD = 13 should have the following properties:
- They should have a common factor of 13
- Their remaining factors should multiply to 78/13 = 6

Now, let's identify the possible pairs of natural numbers:

Pair 1: 78 and 13
- The GCD is 13
- The LCM is 78

Pair 2: 26 and 39
- The factors of 26 are 2 x 13
- The factors of 39 are 3 x 13
- The GCD is 13
- The LCM is 2 x 3 x 13 = 78

Therefore, the correct answer is option 'D': 78 and 13, and 26 and 39.
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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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