2020/023) The lowest common multiple of 5 positive integers is 194040. Find the minimum possible sum of these 5 numbers.

The prime factorization of 194040 is:

$194040 = 2^3 ⨯ 3^2 ⨯ 5 ⨯ 7^2 ⨯ 11$

There are 5 numbers which are co-prime to one another.

For the sum of 5 numbers to be lowest the 5 numbers have to be co-prime, The rationale is that each prime factor should have the highest power in at least one number. Say it is x ( x is one of 2,3,5,7,11) Now if it has got any other factor the number becomes bigger and hence the sum

So the numbers are $2^3=8,3^2=9,5, 7^2= 49,11$ and sum is $8+9+5+49+11=82$