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a-b-c-N-5a-6b-9c-abc-min-




Question Number 188156 by Shrinava last updated on 26/Feb/23
a,b,c∈N  5a = 6b = 9c  (abc)_(min)  = ?
a,b,cN5a=6b=9c(abc)min=?
Answered by mr W last updated on 26/Feb/23
5a = 6b = 9c=n  5a = 2×3b = 3^2 c=n  ⇒n_(min) =5×2×3^2 =90  [or n_(min) =lcm(5,6,9)=90]  ⇒a_(min) =((90)/5)=18  ⇒b_(min) =((90)/6)=15  ⇒c_(min) =((90)/9)=10  ⇒(abc)_(min) =18×15×10=2700 ✓
5a=6b=9c=n5a=2×3b=32c=nnmin=5×2×32=90[ornmin=lcm(5,6,9)=90]amin=905=18bmin=906=15cmin=909=10(abc)min=18×15×10=2700
Commented by Shrinava last updated on 26/Feb/23
cool dear professor thankyou
cooldearprofessorthankyou

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