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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
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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; 2x 3 x 5     180 pf; 2x 32 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

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