GCD&LCM of three

GCD of three numbers is 30 and LCM is 900. As two the are 60 and 150, find the number.

Final Answer:

c =  180

Step-by-step explanation:

GCD(a,b,c)=30 LCM(a,b,c)=900  a=60 b=150 c=?  60 = 2 × 2 × 3 × 5 = 22 × 3 × 5 150 = 2 × 3 × 5 × 5 = 2 × 3 × 52 GCD(60, 150) = 2×3​ × 5 = 30 LCM(60, 150) = 22 × 3 × 52 = 300  c=60⋅ 3=180   Verifying Solution:  180 = 2 × 2 × 3 × 3 × 5 = 22 × 32 × 5  GCD(60, 150, 180) = 2 × 3 × 5 = 30 LCM(60, 150, 180) = 22 × 32 × 52 = 900

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