Question

Counting the number of rose cuttings, Anisha realized that she can plant these roses exactly in rows of 12 or 15. Find the number of rose cuttings she had if the number was between 100 and 150.

Answer 1

Rose cuttings can be planted exactly in rows of 12 or 15.
$\Rightarrow$ Number of rose cutting is a common multiple of 12 and 15.
LCM (12,5) =$3\times 5\times 4=60$
$\therefore$ Common multiples of 12 and 15 are
$60,60\times 2=120,60\times 3=180,60\times 4=240,...$
Since the number of rose cutting lie between 100
and 150, the number of rose cuttings =120
$\begin{array}{cc}3& 12,15\\ 5& 4,5\\ 4& 4,1\\ & 1,1\end{array}$