Question

Find the smallest whole number which is divisible by
$1\frac{1}{2},2\frac{1}{2},1\frac{1}{3},2\frac{1}{4}$

• A. $144$
• B. $216$
• C. $180$
• D. $252$

Answer 1

The correct option is C $180$

$1\frac{1}{2},2\frac{1}{2},1\frac{1}{3},2\frac{1}{4}$
$=\frac{3}{2},\frac{5}{2},\frac{4}{3},\frac{9}{4}$
The smallest whole number divisible by $1\frac{1}{2},2\frac{1}{2},1\frac{1}{3},2\frac{1}{4}$ is the L.C.M of $1\frac{1}{2},2\frac{1}{2},1\frac{1}{3},2\frac{1}{4}$
$\therefore L.C.M=\frac{L.C.Mofnumerator}{H.C.Fofdenominator}$
$=\frac{L.C.Mof3,5,4,9}{H.C.Fof2,2,3,4}$
$=\frac{3\times 5\times 4\times 3}{1}$
$=180$