- RAJASUMAN PEDDI
- Nov 14, 2016

If a,b, and c are positive integers. What is the minimum value of abc if 2a = 3b = 5c?

**Option:**

**a**. 900

**b**. 600

**c**. 30

**d**. 300

**Solution:**

It is given that a, b, and c are integers and 2a = 3b = 5c

a = 3b / 2 ; a = 5c / 2

b= 2a / 3 ; b = 5c / 3

c = 2a / 5 ; c = 3b / 5

Using above equations, it can be found that *a* has to be a multiple of 2 and 5, b has to be a multiple of 3 and 5 , and c has to be a multiple 2 and 3 for a, b, and c to be a integer.

Therefore, we take L.C.M of 2,3, and 5.

L.C.M of 2,3, and 5 = 30

Rewrite the equation as 2a = 3b = 5c = 30k

a = 15k

b = 10k

c = 6k

abc = 15k x 10k x 6k = 900k^{3}

so, abc will be minimum when k = 1.

Therefore, the minimum value of abc = 900

**Hence, option A is correct.**

Try to solve this question on your own! Do post your comments and solutions in the comment section below.

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