Question

find the LCM and HCF of 120 and 144 using fundamental theorem of arithmetic​

Answer 1

Answer:

120=2^3×3×5

144=2^4×3^2

hcf= 2^3×3

=8×3

=24

lcm= 2^4×3^2×5

=16×9×5

=720

so, hcf =24 and lcm = 720

Answer 2

${\mathfrak{\red{\underline{\underline{Answer:-}}}}}$

$\sf{L.C.M.\;of\;120\;and\;144\;is\;720}$

$\sf{H.C.F.\;of\;120\;and\;144\;is\;24}$

${\mathfrak{\red{\underline{\underline{Explanation:-}}}}}$

$\begin{array}{r | l}2 & 120 \\\cline{2-2} 2 & 60 \\\cline{2-2} 2 & 30 \\\cline{2-2} 3 & 15 \\\cline{2-2} 5 & 5 \\\cline{2-2} & 1\end{array}$

$\begin{array}{r | l}2 & 144 \\\cline{2-2} 2 & 72 \\\cline{2-2} 2 & 36 \\\cline{2-2} 2 & 18 \\\cline{2-2} 3 & 9 \\\cline{2-2} 3 & 3 \\\cline{2-2} & 1\end{array}$

$\sf{\therefore 120=2\times2\times2\times3\times5=2^{3}\times3\times5}$

$\sf{\therefore 144=2\times2\times2\times2\times3\times3=2^{4}\times3^{2}}$

$\sf{Therefore,\;L.C.M.\;of\;120\;and\;144\;is\;2^{4}\times3^{2}\times5=720.}$

$\sf{And\;H.C.F.\;of\;120\;and\;144\;is\;2^{3}\times3=24.}$