Question-116658

Question Number 116658 by zakirullah last updated on 05/Oct/20

Commented by Rasheed.Sindhi last updated on 08/Oct/20

A n O ther W ay ↶ \underset{↓}{↑} ↷

12 = 2^{2} . 3

T h e s m a l l e s t p e r f e c t s q u a r e

d i v i s i b l e b y 12 : 2^{2} . 3.3 = 36

16 = 2^{4}

T h e s m a l l e s t p e r f e c t s q u a r e

d i v i s i b l e b y 16 : 2^{4} = 16

20 = 2^{2} . 5

T h e s m a l l e s t p e r f e c t s q u a r e

d i v i s i b l e b y 20 : 2^{2} . 5.5 = 100

24 = 2^{3} . 3

T h e s m a l l e s t p e r f e c t s q u a r e

d i v i s i b l e b y 24 : 2^{3} . 3.2.3 = 144

T h e s m a l l e s t p e r f e c t s q u a r e

n u m b e r w h i c h i s d i v i s i b l e

b y 12, 16, 20 & 24 :

LCM (36, 16, 100, 144) = 3600

Commented by zakirullah last updated on 08/Oct/20

t h a n k s o m u c h s i r

Answered by mr W last updated on 05/Oct/20

12 = 2^{2} \times 3

16 = 2^{4}

20 = 2^{2} \times 5

24 = 2^{3} \times 3

\Rightarrow 2^{4} \times 3^{2} \times 5^{2} = 3600

Commented by zakirullah last updated on 05/Oct/20

t h a n k s a l o t

Commented by zakirullah last updated on 05/Oct/20

s i r h o w 5^{2} c o m e s

Commented by JDamian last updated on 05/Oct/20

it is on purpose. Otherwise the number wouldn't be a perfect squared. In fact, all the primes of the number must be present as an even power.

Answered by $@y@m last updated on 05/Oct/20

12 = 2 \times 2 \times 3

16 = 2 \times 2 \times 2 \times 2

20 = 2 \times 2 \times 5

24 = 2 \times 2 \times 2 \times 3

A l l e x c e p t 5 h a v e p a i r .

T h e r e f o r e r e q u i r e d n o . i s

2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 = 3600

Commented by zakirullah last updated on 05/Oct/20

s i r a n s i s 3600

Commented by zakirullah last updated on 05/Oct/20

t h a n k s