Question

find the smallest square number divisible by each one of the number 8 9 and 10​

Answer 1

Answer:

LCM of 8 9 and 10 is 360

prime factorisation of 360 is 2 × 2 × 2 × 3 × 3 × 5

next make pairs of numbers

= (2 × 2) × (3 × 3) × 2 × 5

two numbers are left so multiply so that they can become a pair,

(2 × 2) × (2 × 2) × (3 × 3) × (5 × 5)

= 4 × 4 × 9 × 25

= (4 × 25) × (4 × 9)

= 100 × 36

= 3600

so, the smallest square number divisible by 8 9 and 10 is 3600.

Answer 2

Answer:

Least Square is 3600.

Step-by-step explanation:

We need to find Smallest Square number divisible by 8 , 9 , 10

Prime Factorization of 8 , 9 , 10

8 = 2 × 2 × 2

9 = 3 × 3

10 = 2 × 5

LCM of 8 , 9 , 10 = 2 × 2 × 2 × 3 × 3 × 5 = 360

Clearly smallest number divisible by 8 , 9 and 10 is 360 but it is not a perfect square number.

Now to find least Square number we complete the pairs we complete the pairs which are single in prime factorization of LCM

one 2 and one 5 is need to complete the pair.

We get, Least Square number = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 3600

Therefore, Least Square is 3600.