Question

The HCF and LCM of two numbers
are 13 and 455 respectively. If one
of the numbers lies between 75 and
125, then, that number is :
दो संख्याओं का म.स. व ल.स. क्रमशः 13 तथा
455 है। यदि एक संख्या 75 तथा 125 के बीच
है, तो वह संख्या क्या है?
(a) 78 (b) 91
(c) 104 (d) 117
​

Answer 1

91

HCF = 13

Let the numbers be 13x and 13y, where x and y are co-prime to each other.

∴ LCM = 13xy

∴ 13xy = 455

\therefore xy = \frac{455}{13} = 35 = 5\times 7

∴ Numbers are 13 \times 5 = 65 and 13 \times 7 = 91

Hence option [B] is correct answer.

Answer 2

Let the nos. be 13a and 13b

where a and b are coprime

we know that LCM ×HCF=product of two nos. therefore we have,

13a*13b=13×455

169ab=5915

ab=35

two coprime nos. with product 35 are 5 and 7

therefore the required no.=(13*5,13*7)=(65,91)

hence the no. that lies between 75 and 125 is 91