Question

Find the least square number which is divisible by each of the number 4,8,12.​

Answer 1

Answer:

Step-by-step explanation:

For any number to be exactly divisible by 4,8, and 12, that number has to be exactly divisible by the L.C.M. of those three numbers.

Now 4 = 2^2, 8 = 2^3 and 12 = 2^2 . 3

Therefore, L.C.M. of 4, 8 and 12 = 2^3 . 3 = 24

To find that number which is the smallest square number, we will take integral multiples of the L.C.M. and check for the squareness of each of the multiples so obtained at every step. The first number that will be a square will be the smallest square number.

24 x 1 = 24 (not a square)

24 x 2 = 48 (not a square)

24 x 3 = 72 (not a square)

24 x 4 = 96 (not a square)

24 x 5 = 120 (not a square)

24 x 6 = 144 = 12^2

Therefore, since 144 is the square of 12, 144 is the smallest square number which is divisible by 4, 8, and 12 (Proved).

Answer 2

SOLUTION

TO DETERMINE

The least square number which is divisible by each of the number 4 , 8 , 12

CONCEPT TO BE IMPLEMENTED

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

EVALUATION

Here the given numbers are 4 , 8 , 12

We now prime factorise the given numbers

4 = 2 × 2

8 = 2 × 2 × 2

12 = 2 × 2 × 3

LCM of the numbers

= 2 × 2 × 2 × 3

= 2² × 2 × 3

= 24

We see that one 2 and one 3 is left of the pair

So we need to multiply the LCM with 2 , 3 to get the least square number

Hence the required least square number

= 2² × 2² × 3²

= 4 × 4 × 9

= 144

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