Question

Find the L.C.M and H.C.F. of 1296 and 2520 by applying the fundamental theorem of arithmetic method i.e. using the prime factorisation method. [3 MARKS]

Answer 1

Prime factorisation : 1 Mark
H.C.F : 1 Mark
L.C.M : 1 Mark

$1296=2\times 2\times 2\times 2\times 3\times 3\times 3\times 3=2^4\times 3^4$ $2520=2\times 2\times 2\times 3\times 3\times 5\times 7=2^3\times 3^2\times 5\times 7$
$\begin{array}{cc}2& 1296\\ 2& 648\\ 2& 324\\ 2& 162\\ 2& 81\\ 3& 27\\ 3& 9\\ & 3\end{array}$
$\begin{array}{cc}2& 2520\\ 2& 1260\\ 2& 630\\ 3& 315\\ 3& 105\\ 5& 35\\ & 7\end{array}$

L.C.M. = $2^4\times 3^4\times 5\times 7=45360$

H.C.F. = $2^3\times 3^2=72$