Question

if gcd of two 4 digit numbers is 5 times the sum of their uncommon factors and LCM of the number is 143 times its gcd then find the numbers

Answer 1

Let me first clear it LCM=common factors(HCF) * uncommon factors
Lets gcd be G
and LCM be L
So L=143*G
143 is a multiple of 11 and 13
So one of the two numbers contains 11 while other contains 13
IE. Uncommon factors.
Sum of uncommon factors= 24
Gcd=5*24=120
Lcm=143*120
The two numbers are 11*120 and 13*120
=1320 and 1560