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:

$100,150$ and $200$

Answer 1

Step 1: Use the prime factor method to find $L.C.M$

$L.C.M$ of $100,150$ and $200$
Prime factors of $100=2\times 2\times 5\times 5$
$=2^2\times 5^2$
Prime factors of $150=2\times 3\times 5\times 5$
$=2^1\times 3^1\times 5^2$
Prime factors of $200=2\times 2\times 2\times 5\times 5$
$=2^3\times 5^2$ (1 mark)
$\therefore L.C.M.$ of $100,150$ and $200$
$=2^3\times 3^1\times 5^2$
$=2\times 2\times 2\times 3\times 5\times 5$
$=600$ (1 mark)

Step 2: Use the common division method to find $L.C.M.$
(1 mark)
$L.C.M.$ of $100,150$ and $200=2\times 2\times 2\times 3\times 5\times 5$
$=600$ (1 mark)