If m and n are positive integers such that \(\gcd(m,n) = 12\) , then what is the smallest possible value of \(\gcd(10m,15n) = ?\)

tertre
Mar 19, 2017

#1**+1 **

gcd(m,n) = 12 the two smallest numbers that are divisble by 12 that are different are 12 and 24

we will switch these areound for a smaller number m=24 n=12

10 times 24 = 240 and 15 times 12 is 180

240 pf; 2^{4 }x 3 x 5 180 pf; 2^{2 }x 3^{2 }x 5 similar pf's = 2x2x3x5 which is equal to 60

60 is your answer!

if I helped please leave a rating

pf= prime factor

HelpMeWithThisPlease
Mar 20, 2017