Question

.Two 2-digit numbers have hcf13 and lcm is 156. Which of the following is the largest number​

Answer 1

Answer:

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I would rather use a different approach.

As the HCF of both the numbers is 13 , both the numbers can be expressed as 13x and 13y ,

where both x and y are coprimes. If this is not the case, it means there is common factor, k for both x and y. Under such circumstances HCF would be 13k.

As the numbers are 2 two digit numbers, 0 <x,y<8.

Since the product is 2028,

13x∗13y=2028

x∗y=12

The possible combinations for x and y are (1 ,12),(2,6),(3,4) .

Since the x,y pair has to be coprimes, the required combinations are (x ,y)=(1,12)or(3,4).

And also the restriction is that both x and y should be less than 8 .

This reduces to single possibility for x,y pair (3,4) , giving us 39 and 52 as the required numbers.

Hope my explanation is simple.