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

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 \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