Question

250 and 336,Find g.c.d. and Lc.m. using the fundamental theorem of arithmetic.

Answer 1

FUNDAMENTAL THEOREM OF ARITHMETIC : Every composite number can be expressed( factorized) as a product of primes and this factorization is unique except for the order in which the prime factors occur.

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 :

250 and 336

Prime factors of 250 = 2¹ × 5³

Prime factors of 336 = 2⁴ × 3¹ × 7¹

GCD (250 and 336) = 2¹ = 2

LCM (250 and 336) = 2⁴ × 5³ × 3¹× 7¹ =16 × 125 × 3× 7= 42000

LCM (250 and 336) = 42000

Hence, the GCD is 2 & LCM is 42000

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi ,

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

Fundamental Theorem of Arithmetic:

Every composite number can be

expressed as a product of primes ,

and this factorisation is unique , apart

from the order in which the prime factors

occur .

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

250 = 2 × 5 × 5 × 5 = 2¹ × 5³

336 = 2 × 2 × 2 × 2 × 3 × 7

= 2⁴ × 3¹ × 7¹

HCF ( 250 , 336 ) = 2¹

[ Product of the smallest power of

each common prime factors of the

numbers ]

LCM ( 250 , 336 ) = 2⁴ × 3 × 5³ × 7

[ Product of the greatest power

of each prime factors of the numbers ]

= 42000

Therefore ,

HCF = 2 ,

LCM = 42000

I hope this helps you.

: )