Question

Smallest square number that is divisible by each of 5 and 11

Answer 1

Step-by-step explanation:

Answer:-

Answer:-55

55 is the smallest square number that is divisible by each of 5 and 11

${55}^{2} = 3025$

Answer 2

Answer:

The smallest square number is $55^2$ that is divisible by 5 and 11.

Step-by-step explanation:

Observe that the numbers 5 and 11 both are prime numbers.

Factorisation of 5 is:

5 = 5 × 1

Factorisation of 11 is:

11 = 11 × 1

Thus, L.C.M of 5 and 11 is:

= 5 × 11 × 1

= 55

Thus, 55 is the smallest positive integer divisible by 5 and 11.

⇒ Square of 55 is also divisible by both 5 and 11, i.e.,

⇒ 5 divides $55^2$, i.e.,

⇒ $\frac{55^2}{5}=\frac{55\cdot 55}{5}$

         $=11\cdot 55$

         = 605

Similarly,

11 divides $55^2$, i.e.,

⇒ $\frac{55^2}{11}=\frac{55\cdot 55}{11}$

         $=5\cdot 55$

         = 275

Therefore, the smallest square number is $55^2$ that is divisible by 5 and 11.

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