Question

Find the L.C.M and H.C.F. of 864 and 2520 by applying the fundamental theorem of arithmetic method i.e. using the prime factorisation method.

Answer 1

Given, numbers are 864 and 2520.
So,
$864=2\times 2\times 2\times 2\times 2\times 3\times 3\times 3=2^5\times 3^3$ $2520=2\times 2\times 2\times 3\times 3\times 5\times 7=2^3\times 3^2\times 5\times 7$
$\begin{array}{cc}2& 864\\ 2& 432\\ 2& 216\\ 2& 108\\ 2& 54\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$
$\begin{array}{cc}2& 2520\\ 2& 1260\\ 2& 630\\ 3& 315\\ 3& 105\\ 5& 35\\ & 7\end{array}$

L.C.M. = $2^5\times 3^3\times 5\times 7=30240.$

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