Question

By using set theory find lcm and hcf of 48 and 72 and 24

Answer 1

The LCM and HCF of the three given integer numbers are 24 and 144 respectively.

Given

The three integer numbers are 24,48 and 72

To find:

The LCM and HCF of the three numbers.

Solution:

We have to calculate the Lowest common multiple and the Highest common factor of the three numbers that are represented here.

So we have to use the prime factorization of all the numbers:

$24 = 2^3\times 3\\\\48 = 2^4\times 3\\\\72=2^3\times 3^2$

Now for the highest common factor we will take all the factor that are common to the three numbers.

$\text {H.C.F} =(2^3\times 3)= 24$

Therefore the HCF of the three number is 24.

Now for lowest common multiple we take all the common factors and then we take the excess factors.

$\text {L.C.M} =(2^3\times 3\2 \times 3)= 144$

Hence the LCM of the three numbers is 144.

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