The-LCM-and-the-GCF-of-three-intergers-are-180-and-3-respectively-Two-numbers-are-45-and-60-What-is-the-third-number-

Question Number 41167 by Cheyboy last updated on 02/Aug/18

T h e L C M a n d t h e G C F o f t h r e e

i n t e r g e r s a r e 180 a n d 3 r e s p e c t i v e l y .

T w o n u m b e r s a r e 45 a n d 60 .

W h a t i s t h e t h i r d n u m b e r

Answered by MJS last updated on 02/Aug/18

45 = 3^{2} 5

60 = 2^{2} 3 \times 5

lcm (45, 60) = 2^{2} 3^{2} 5 = 180

lcm (180, x) = 180

\Rightarrow x = 2^{0 ⩽ i ⩽ 2} 3^{0 ⩽ j ⩽ 2} 5^{0 ⩽ k ⩽ 1}

gcf (45, 60) = 3 \times 5 = 15

gcf (15, x) = 3

\Rightarrow x = 2^{0 ⩽ i} 3^{1 ⩽ j}

\Rightarrow x \in {3, 6, 9, 12, 18, 36}

Commented by Cheyboy last updated on 02/Aug/18

T h a n k y o u s i r . I t h o u g h i t w a s o n l y 3

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