Question

The least number which is a perfect square and is divisible by each of $16,20and24$ is:

Answer 1

Step 1: Find the $LCMOF16,20and24$

Prime factorisation of $16=2x2x2x2=2^4$

Prime factorisation of $20=2x2x5=2^2\times 5$

Prime factorisation of $24=2x2x2x3=2^3\times 3$

Now, to find LCM , we need to multiply all the prime factors that has occurred the maximum number of times in either of the numbers.

So, $LCM(16,20,24)=2^4\times 3\times 5=240$

Step 2: Check the number making pairs and multiply numbers that are not in pairs

we know that for a number to be a perfect square each factor should be in pair of two or in even numbers ,Here we can see that $3and5$ are not in pair of two . So, to get the number , we will multiply $3and5$ to the LCM obtained.

So, the required least number which is a perfect square and divisible by $16,20and24is3600.$