Question

4. The least square number exactly divisible by each one of the numbers 6, 8 and 16 is

(a) 96

(b) 144

(c) 64

(d) 36

also explain plz..​

Answer 1

Answer:

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Answer 2

Answer:

Solution :-

As we know that, to find the least Number which can be exactly divisible by each one of the given numbers is LCM of all the given Numbers.

So,

Prime Factors of 6, 8 and 16 :-

→ 6 = 2¹ * 3¹

→ 8 = 2 * 2 * 2 = 2³

→ 16 = 2 * 2 * 2 * 2 = 2⁴

LCM :- 2⁴ * 3

Now, we have to find Least Square number .

we know that, any number to be a perfect Square , it must be pair of Prime factors .

So, in LCM = 2⁴ * 3 = 2² * 2² * 3 as we can 3 is only one time.

we can conclude that, we must multiply the LCM with 3 in order to make it a perfect Square.

Therefore,

→ Required Number = 2² * 2² * 3 * 3 = 4 * 4 * 9 = 144 (Ans.)

Hence, 144 is the Least square number exactly divisible by each one of the numbers 6,8,16.