Question

find the smallest square number which can be completely divided by 6 10 and 12
pls explain briefly ​

Answer 1

Step-by-step explanation:

Complete step-by-step answer:

We know LCM of three numbers can be calculated by writing the numbers in their prime factorization.

6=2×39=3×315=3×5

So to find the LCM we will take the highest number of times whichever prime is repeated and multiply with other primes.

We have 2 only one time, 3 is multiplied two times so we take 3×3

and 5 is also there one time.

SO, LCM is 2×3×3×5=90

Now we know prime factorization of 90=2×3×3×5

To find the smallest number that is a square and is divisible by 90 we will form a number by multiplying factors to the prime factorization of 90.

So, to make 2×3×3×5

a square we need each number to be multiplied to itself. i.e. each prime factor should be in square.

We can write the prime factors in the form of their powers as

⇒2×3×3×5=21×32×51

Answer 2

Step-by-step explanation:

Transcript

Solution:

L.C.M. of 4, 9 and 10 is 180.

Prime factors of 180 = 2 x 2 x 3 x 3 x 5

Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.

\therefore180\times5=900

Hence, the smallest square number which is divisible by 4, 9 and 10 is 900.