Question

find the smallest square number that is divisible by each of the numbers 4,9 and 10​

Answer 1

Step-by-step explanation:

360

please brainliest this answer

Answer 2

Answer:

Given:-

Numbers

To find:-

Smallest number dividend divisible by each of the given numbers.

Find the LCM(Lowest common multiple)of the given numbers:-

• ⇴LCM is the number that is perfectly divisible by each one of 4,9,10.
• ⇴LCM is found by the common multiples of their prime factorization.

(I)Prime factor of 4,

4=(2×2)×1

2 is common pair

(II)Prime factor of 9,

9=(3×3)×1

3 is the common pair

(III)Prime factor of 10,

10=2×5×1

No common pair

Multiplying the LCM by the unpaired number i.e. 5 will make it a perfect square.

∴The square number required=180×5=900

It's square root equals to:

$\small\sf{900 = (2 \times 2) \times (3 \times 3) \times (5 \times 5)} \\ \small\sf{ \therefore \: \sqrt{900} = 2 \times 3 \times 5 = 30 }$

Hence,900 is the required smallest square number.