The-LCM-and-GCF-of-three-numbers-is-360-and-6-respectively-if-the-two-numbers-are-18-and-60-find-the-third-number-

Question Number 33089 by mondodotto@gmail.com last updated on 10/Apr/18

T he LCM and GCF of three numbers is

360 and 6 respectively . if the

two numbers are 18 and 60 .

find the third number .

Commented by Rasheed.Sindhi last updated on 10/Apr/18

24, 72, 120, 360

Commented by mondodotto@gmail.com last updated on 10/Apr/18

please show workings

Commented by mondodotto@gmail.com last updated on 10/Apr/18

please help

Commented by mondodotto@gmail.com last updated on 10/Apr/18

solution please

Commented by mondodotto@gmail.com last updated on 10/Apr/18

also answers are not true because i have tried to prove i get LCM = 720 instead of 360 but GCF is correct

Answered by MJS last updated on 10/Apr/18

18 = 2 \times 3^{2}

60 = 2^{2} \times 3 \times 5

6 = 2 \times 3 \Rightarrow x = 2^{l} \times 3^{m}; l, m > 0

360 = 2^{3} \times 3^{2} \times 5 \Rightarrow x = 2^{3} \times 3^{m} \times 5^{n}; 0 ⩽ m ⩽ 2; 0 ⩽ n ⩽ 1

x_{1} = 2^{3} \times 3 = 24

x_{2} = 2^{3} \times 3^{2} = 72

x_{3} = 2^{3} \times 3 \times 5 = 120

x_{4} = 2^{3} \times 3^{2} \times 5 = 360

Commented by mondodotto@gmail.com last updated on 10/Apr/18

120 and 360 proved correct

but 24 and 72 are not

Commented by MJS last updated on 10/Apr/18

then your proof is wrong

the g c d (18; 60; x); x \in {24; 72; 120; 360}

is 6 because the g c d (18; 60) = 6

and it {can}^{'} t get higher adding

a 3^{rd} number

l c m (18; 24; 60) =

= l c m (2 \times 3^{2}; 2^{3} \times 3; 2^{2} \times 3 \times 5) = 360

l c m (18; 60; 72) =

= l c m (2 \times 3^{2}; 2^{2} \times 3 \times 5; 2^{3} \times 3^{2}) = 360

l c m (18; 60; 120) =

= l c m (2 \times 3^{2}; 2^{2} \times 3 \times 5; 2^{3} \times 3 \times 5) = 360

l c m (18; 60; 360) =

= l c m (2 \times 3^{2}; 2^{2} \times 3 \times 5; 2^{3} \times 3^{2} \times 5) = 360

Commented by mondodotto@gmail.com last updated on 10/Apr/18

thanx now i understand

Commented by MJS last updated on 10/Apr/18

{you}^{'} re welcome

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