A number lies between the cubes of 11 and 12. If the number is divisible by twice of 80 and 6 both, what will be the number?

Correct option is D

Given:

The number lies between the cubes of 11 and 12

It is divisible by both twice of 80 and 6

Solution:

Cubes:  11³ = 1331,12³ = 1728

Twice of 80 = 160, Other divisor = 6

Prime factorization:

160 = 2^5 \times 5

6 = 2 \times 3

So,

LCM(160,6) = 2^5 \times 3 \times 5 = 480

Now, the smallest multiple of 480 that lies between 1331 and 1728:

480 × 2 = 960(too small)

480 × 3 = 1440(valid)

480 × 4 = 1920(>1728,invalid)

Thus, Option(D) 1440 is correct.