Question

If $x=2^3\times 3\times 5^2$, $y=2^2\times 3^3$, then the $LCM(x,y)$ is

Answer 1

LCM by Prime factorization method

Step I:
$\text{Resolve each given number into its prime factors and express the factors obtained in exponent form.}$

Step I:
$\text{Find the product of the highest powers of all the factors that occur in any of the given numbers.}$

Step III:
$\text{The product obtained in Step II is the required least common multiple (L.C.M).}$

Here,

$\Rightarrow x=2^3\times 3\times 5^2,y=2^2\times 3^3$

$\Rightarrow LCM(x,y)=2^3\times 3^3\times 5^2$

$\Rightarrow LCM(x,y)=5400$