Find the g.c.d. and l.c.m. using the fundamen | vedclass

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Question

(A) First,we find the prime factorization of each number:
$24 = 2 	imes 2 	imes 2 	imes 3 = 2^{3} 	imes 3^{1}$
$36 = 2 	imes 2 	imes 3 	imes

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(A) First,we find the prime factorization of each number:
$24 = 2 	imes 2 	imes 2 	imes 3 = 2^{3} 	imes 3^{1}$
$36 = 2 	imes 2 	imes 3 	imes 3 = 2^{2} 	imes 3^{2}$
$60 = 2 	imes 2 	imes 3 	imes 5 = 2^{2} 	imes 3^{1} 	imes 5^{1}$
The $g.c.d.$ (Greatest Common Divisor) is the product of the smallest power of each common prime factor:
$g.c.d. (24, 36, 60) = 2^{2} 	imes 3^{1} = 4 	imes 3 = 12$
The $l.c.m.$ (Least Common Multiple) is the product of the highest power of each prime factor involved:
$l.c.m. (24, 36, 60) = 2^{3} 	imes 3^{2} 	imes 5^{1}$
$= 8 	imes 9 	imes 5 = 360$
Thus,the $l.c.m.$ is $360$.

Find the $g.c.d.$ and $l.c.m.$ using the fundamental theorem of arithmetic for the numbers: $24$,$36$,and $60$.

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