Question

Find the $L.C.M.$ of each of the following groups of numbers, using (i) the prime factor method (ii) the common division method:

(v) $34,85$ and $51$

Answer 1

Step 1: Use the prime factor method to find $L.C.M.$
$L.C.M.$ of $34,85$ and $51$
Prime factors of $34=2\times 17=2^1\times {17}^1$
Prime factors of $85=5\times 17=5^1\times {17}^1$
prime factors of $51=3\times 17=3^1\times {17}^1$
$\therefore L.C.M.$ of $34,84$ and $51=2^1\times 5^1\times 3^1\times {17}^1$
$=2\times 3\times 5\times 17=510$

Step 2: Use the common division method to find $L.C.M.$

$L.C.M.$ of $34,85$ and $51=2\times 3\times 5\times 17=510$