What is the smallest cubic number, which is divisible by 72,108 and 300?

Question

Question

This question was previously asked in

RRB NTPC CBT 2 (Level-5) Official Paper (Held On: 12 June 2022 Shift 1)

Answer 1

Given:

The number should be divisible by 72, 108, and 300

Concept used:

For this type of question, we use the LCM method to find the required number

Calculation:

72 = 2³ × 3²

108 = 2² × 3³

300 = 2²×3 × 5²

LCM= 2³ × 3³ × 5²

⇒ 5400

Now the number should be a cubic number and multiple of 5400

So,

5400 × 2 = 10800 which is not a cubic number

5400 × 3 = 16200 which is not a cubic number

5400 × 5 = 27000 which is a cubic number and the smallest

∴ The smallest cubic number, divisible by 72,108 and 300 is 27000.