Question

i want the answer with explanation plzzz it's urgent.... ​

Answer 1

the fundamental theorem of arithmetic is that every composite number can be expressed uniquely as product of primes. From this theorem has the concept of prime factorisation of number come into play to find HCF and LCM of given numbers.

In fact, the long division method is also based on euclid division algorithm.

all we need to do here is to find HCF and LCM of given numbers using prime factorisation

the numbers are 625,. 1125,. 2125

prime factorisation of

625 = 5 x 5 x 5 x 5

1125 = 3 x 3 x 5 x 5 x 5

2125 = 5 x 5 x 5 x 17

now HCF will be product of all such prime numbers which are present in all the three factorisation

HCF = 5 x 5 x 5 = 125

LCM will be product of each type of prime numbers taking their maximum presence in any one of the factorisations

LCM = 3 x 3 x 5 x 5 x 5 x 5 x 17

= 95625