Question

by smallest number must 180 multiplies so becomes a perfect cubes

Answer 1

By prime factorisation  

2 180

2 90

3 45

3 15

5 5

1

5 is left unpaired

So 5 is the smallest number  

180×5=900

hope u like...................................

Answer 2

Hey mate here is the answer.


We know that a no. is aperfect cube when is all prime factors are in triplets.

By prime factorization
180=2×2×3×3×5
Here we find that the prime factor of 180,
2 and 3 occur twice and 5 occur once.
If we multiply 180 with (2×3×5×5)
then the product would be=2×2×3×3×5×2×3×5×5
i.e 2×2×2×3×3×3×5×5×5
which is a perfect cube (as all the prime factors occur in triplets)

therefore,150 (2×3×5×5) is the smallest no. by which 180 must be multiplied so that the product became a perfect cube.

Thnq 4 asking question.