Question

225 and 145,Find g.c.d. and Lc.m. using the fundamental theorem of arithmetic.

Answer 1

GCD (Greatest common divisior) (HCF) (Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.

LCM (least common multiple) of two or more numbers = product of the highest Power of each factor involved in the numbers.

SOLUTION :

225 and 145

Prime factors of 225 = 3² × 5²

Prime factors of 145 = 5 × 29

GCD (225 and 145) = 5

LCM (225 and 145) = 3² × 5² × 29 = 9× 25 ×29

LCM (225 and 145) = 6525

Hence, the GCD is 5 & LCM is 6525

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi ,

*****************************************

Fundamental Theorem of Arithmetic :

Every composite number can be

expressed ( factorised ) as a product

of primes , and this factorisation is

unique , apart from the order in which

the prime factors occur .

****************************************

225 = 3 × 3 × 5 × 5 = 3² × 5²

145 = 5 × 29

HCF ( 225 , 145 ) = 5

[ Product of the smallest power of

each common prime factors of the

numbers ]

LCM ( 225 , 145 ) = 3² × 5² × 29

[ Product of the greatest power of each

prime factors of the numbers ]

= 6525

Therefore ,

HCF = 5

LCM = 6525

I hope this helps you.

: )