Question

What is the smallest number by which 1372 must be multiplied so that the product
becomes a perfect cube? Find the required perfect cube so obtained.​

Answer 1

Answer:

heyyyoo ....the smallest number by which u should multiply 1372 is 2

Step-by-step explanation:

firstly , prime factorize the number given in the question ( 1372 )

then , form groups of 3 ( as the question asks for cube)

the number left out will be your answer ....like in this case it was 2 as the 7's got grouped ( see the pic ) ...therefore if u multiply 1372 with 2 ...u will get a perfect cube .

hope it helps u !! please mark me a s brianliest !!!!

Answer 2

Step-by-step explanation:

Step 1 : We will find the prime factors of 1372 by prime factorisation method

1372 = 2 × 2 × 7 × 7 × 7

Step 2 : Find the least number

If we see, the prime factors of 1372, 7 is in the group of 3 i.e. it makes a cube but 2 is not in a group of 3 i.e. it is not making a cube.

∴ is the smallest number by which 1372 must be multiplied so that the product becomes a perfect cube.

Let's check :

1372 × The least number

➾ 1372 × 2

➾ 2744

= 14

Hence, proved.

Hope it's help you........