Question

If a = 2² × 3^x, b = 2² × 3 × 5, c = 2² × 3 × 7 and LCM (a, b, c) = 3780, then x is equal to ______.

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Answer 1

If a = 2² × 3^x, b = 2² × 3 × 5, c = 2² × 3 × 7 and LCM (a, b, c) = 3780, then x is equal to 3.

Explanation:

Given, LCM (a, b, c) = 3780

To find the LCM, we take the highest power of each prime:

Highest power of 2 is 2².

Highest power of 3 is 3^x.

Highest power of 5 is 5¹.

Highest power of 7 is 7¹.

Therefore, LCM (a, b, c) = 2² × 3^x × 5 × 7

Given, LCM (a, b, c) = 3780

So, 2² × 3^x × 5 × 7 = 3780

4 × 5 × 7 × 3^x = 3780

140 × 3^x = 3780

3^x = `3780/140`

3^x = 27

27 = 3³

x = 3