suppose that a and b are natural numbers whose prime factorizations have no prim

Question

suppose that a and b are natural numbers whose prime factorizations have no primes in common. show that for any natural number m, the product ab divides m if each of a and b divides m
suppose that a and b are natural numbers whose prime factorizations have no primes in common. show that for any natural number m, the product ab divides m if each of a and b divides m
suppose that a and b are natural numbers whose prime factorizations have no primes in common. show that for any natural number m, the product ab divides m if each of a and b divides m

Explanation / Answer

gcd( a , b ) = 1

m divides ab

=> m = k ( ab )

=> m = b ( ka )

=> m = k2 b

=> m divides b

Similarly ,

=> m = k ( ab )

=> m = a ( kb )

=> m = k1 a

=> m divides a

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