Question

How many multiples of the number 2¹³ × 3⁵ × 5³ × 7⁶ are perfect cubes or complete cubes?
1. 24
2. 60
3. 36
4. 48

Answer 1

Correct Answer - Option 2 : 60

The given number is:

213 × 35 × 53 × 76

For each term, the perfect cubes can be obtained as:

For 2¹³ = 2⁰, 2³, 2⁶, 2⁹, 2¹²; i.e. 5 terms

For 3⁵ = 3⁰, 3³; i.e. 2 terms

For 5³ = 5⁰, 5³; i.e. 2 terms

For 7⁶ = 7⁰, 7³, 7⁶; i.e. 3 terms

So, we have the multiples of the number 213 × 35 × 53 × 76 as perfect cubes = 5 × 2 × 2 × 3 = 60 

∴ The number of multiples of the number 213 × 35 × 53 × 76 are perfect cubes or complete cubes, are 60