Question

a, b and c are positive integers. a and b have LCM 30 and GCD 5. Again b and c
have LCM 60 and GCD 3.If a is an even number then find LCM of a and c.

Answer 1

Answer on Question #50080, Math, Other

Task:

a, b and c are positive integers. a and b have LCM 30 and GCD 5. Again b and c have LCM 60 and GCD 3. If a is an even number then find LCM of a and c.

Solution:

$$LMC(a, b) = \frac{a \cdot b}{GCD(a, b)} = \frac{ab}{5} = 30 \Rightarrow ab = 150$$ $$LMC(c, b) = \frac{c \cdot b}{GCD(c, b)} = \frac{cb}{3} = 60 \Rightarrow bc = 180$$ $$150 = 2 \cdot 5 \cdot 3 \cdot 5$$ $$180 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$$ $$\Rightarrow b = 15, \text{ so } a = 10 \text{ and } c = 12.$$ $$LMC(c, a) = \frac{c \cdot a}{GCD(c, a)} = \frac{12 \cdot 10}{2} = 60$$

Answer: LCM(a,c)=60.

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