If a3b = abc = 180, a, b, c are positive integers, then

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180 = 2 × 2 × 3 × 3 × 5
a³b = abc
⇒ a² = c
∴ a³b = abc =180 = 1² × 180 × 1
= 1³ × 180
⇒ c = 1