Question

If the HCF of two mumbers 17and LCM is 1309, which of the given optuons could be one of the numbers
a 167
b 119
c 153
d 170​

Answer 1

Step-by-step explanation:

Given that HCF of two numbers = 17

LCM of two numbers=1309

We know that HCF × LCM= product of two numbers

Now, 17 ×1309= product of two numbers

17 ×17×7×11=product of two numbers

(17×7)×(11×17)=product of two numbers

let A and B be two number

Now , A×B=(17×7)×(17×11)

we can say that A can be(17×7)&B can be (17×11) or A can be (17×11)&B can be(17×7).

clearly,A=119or187

B=187or119

hence, correct option is (b)119

thanks

Answer 2

Given :  HCF of two numbers is 17 and LCM is 1309,

To Find :  what could be one of the two numbers

Solution:

 HCF of two numbers is 17

Hence two numbers are  

17a  and 17b  where a , b are co prime numbers

HCF * LCM  =  Product of numbers

=> 17 * 1309 = 17a * 17b

=> 77 = a * b

77 = 1 * 77 = 7  * 11

a = 1 , 7 , 11 , 77

17a  = 17 , 119  , 187 , 1309

Hence one of the number can be

17 , 119 , 187 , 1309

Hence from the given options 119 is the correct answer.

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