The LCM and GCF of x,18 and 60 are 360 and 6 respectively. find the value of x


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Question Number 41003 by mondodotto@gmail.com last updated on 30/Jul/18

$The LCM and GCF of x, 18 and 60$ $are 360 and 6 respectively .$ $find the value of x$
	Answered by $@ty@m last updated on 31/Jul/18

	$L e t x = 6 k$ $W e h a v e 18 = 6 \times 3$ $60 = 6 \times 10$ $∵ L C M = 360$ $∴ 6 \times k \times 3 \times 10 = 360$ $\Rightarrow k = 2$ $\Rightarrow x = 12$
	Commented by MrW3 last updated on 31/Jul/18

	$L C M f r o m 12, 18 a n d 60 i s 180, n o t$ $360, s o t h e a n s w e r i s n o t c o r r e c t .$
	Commented by mondodotto@gmail.com last updated on 31/Jul/18

	$possible answer not oly 12 there is$ $some other$
	Answered by MJS last updated on 01/Aug/18
	$18=2×3^2 60=2^2 ×3×5 360=2^3 ×3^2 ×5 ⇒ x=2^3 ×3^(0≤j≤2) ×5^(0≤k≤1) 6=2×3 ⇒ x=2^(i≥1) ×3^(j≥1) ×5^(k≥0) i=3 j∈{1, 2} k∈{0, 1} x∈{3, 3^2 , 3×5, 3^2 ×5}×2^3 = ={24, 72, 120, 360}$
	$18 = 2 \times 3^{2}$ $60 = 2^{2} \times 3 \times 5$ $360 = 2^{3} \times 3^{2} \times 5$ $\Rightarrow x = 2^{3} \times 3^{0 ⩽ j ⩽ 2} \times 5^{0 ⩽ k ⩽ 1}$ $6 = 2 \times 3$ $\Rightarrow x = 2^{i ⩾ 1} \times 3^{j ⩾ 1} \times 5^{k ⩾ 0}$ $i = 3$ $j \in {1, 2}$ $k \in {0, 1}$ $x \in {3, 3^{2}, 3 \times 5, 3^{2} \times 5} \times 2^{3} =$ $= {24, 72, 120, 360}$
	Commented by mondodotto@gmail.com last updated on 01/Aug/18

	$thank you sir, blessed$
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