Question

The HCF and LCM of two numbers are 13 and 546 respectively. Find the
possible pairs of the numbers.​

Answer 1

Step-by-step explanation:

The 3 digit factors of 714 :

102 , 119 , 238 , 357 and 714

All of these are also multiples of 17 :

102=6×17

119=7×17

238=14×17

357=21×17

714=42×17

You might notice that 6 has common factor other than 1 with 14 ( 2 ), 21 ( 3 ) and 42 ( 6 ) and 7 also isn’t co-prime with these either, in fact it is one of their factors, but since the highest common factor is 17 we can conclude that 102 and 119 are the wanted numbers.

102+119=221