Find the text{g.c.d.} and text{l.c.m.} of 8,9 | vedclass

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Question

(A) To find the $	ext{g.c.d.}$ and $	ext{l.c.m.}$ using the fundamental theorem of arithmetic,we first find the prime factorization of each number:$

Vedclass · Accepted Answer

g.c.d. = $1$,l.c.m. = $1800$

Vedclass · Answer

(A) To find the $	ext{g.c.d.}$ and $	ext{l.c.m.}$ using the fundamental theorem of arithmetic,we first find the prime factorization of each number:$8 = 2^3$$9 = 3^2$$25 = 5^2$$	ext{g.c.d.}$ is the product of the smallest power of each common prime factor. Since there are no common prime factors,the $	ext{g.c.d.}$ is $1$.$	ext{l.c.m.}$ is the product of the highest power of each prime factor involved:$	ext{l.c.m.} = 2^3 	imes 3^2 	imes 5^2$$	ext{l.c.m.} = 8 	imes 9 	imes 25$$	ext{l.c.m.} = 72 	imes 25 = 1800$.

Find the $\text{g.c.d.}$ and $\text{l.c.m.}$ of $8$,$9$,and $25$ using the fundamental theorem of arithmetic.

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