Matemakak 9432

The cookbook by Matěj Matemakak says:
The greatest common divisor of flour weight and sugar weight is 15, the greatest common divisor of sugar weight and lemon peel weight is 6, the product of sugar weight and lemon peel weight is 1800, and the smallest common multiple of flour weight and sugar weight is 3150.
What are flour, sugar, and lemon peel weights in a lemon pie recipe?

Correct answer:

m =  315 g
c =  150 g
k =  12 g

Step-by-step explanation:

GCD(m,c)=15 GCD(c,k) = 6 c k = 1800 LCM(m,c)=3150  c k = 1800 c1   6   k1   6 = 1800 c1   k1 = 50 c1   k1 = 2 5 5  c1 = fr225 5  5 5 c1=5 5=25 c=6 c1=6 25=150 g  LCM(m,c)=3150 LCM(m,150)=3150 150 = 2 × 3 × 5 × 5 3150 = 2 × 3 × 3 × 5 × 5 × 7  LCM(m, 2 × 3 × 5 × 5)=2 × 3 × 3 × 5 × 5 × 7  m=5 3 3 7=315 g
c=150=150 g
k=1800/c=1800/150=12=12 g   Verifying Solution:  315=3257 150=2352 GCD(315,150)=35=15  t1=GCD(m,c)=GCD(315,150)=15 150=2352 12=223 GCD(150,12)=23=6  t2=GCD(c,k)=GCD(150,12)=6 315=3257 150=2352 LCM(315,150)=232527=3150  t3=LCM(m,c)=LCM(315,150)=3150



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