The LCM of $\frac{3}{8},\frac{5}{16}$ and $\frac{7}{2}$ is:

$52\frac{1}{2}$

LCM of fraction = \(\frac{LCM\;of\;numerator}{HCF\; of\;denominator}\)

The given fractions are :  $\frac{3}{8},\frac{5}{16}$ and $\frac{7}{2}$

LCM of 3, 5, 7 = 105

HCF of 8,16,2 = 2

The LCM of $\frac{3}{8},\frac{5}{16}$ and $\frac{7}{2}$ is = $52\frac{1}{2}$