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Find the smallest cube number which is divisible by 72, 108 and 300?

Find the smallest cube number which is divisible by 72, 108 and 300?
वह छोटी से छोटी घन संख्या ज्ञात कीजिए, जो 72, 108 और 300 से विभाज्य हैं?

27000 21600 3375 5400

Detailed Solution & Logic

Correct Answer:

27000

Solution:

Find LCM of 72, 108, 300

Prime factors:
72 = $2^3 \times 3^2$
108 = $2^2 \times 3^3$
300 = $2^2 \times 3 \times 5^2$

LCM = $2^3 \times 3^3 \times 5^2$

To make it a perfect cube, powers must be multiples of 3:

So multiply by 5:

$= 2^3 \times 3^3 \times 5^3 = (2 \times 3 \times 5)^3 = 30^3$

$30^3 = 27000$

✅ Final Answer: 27000

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