Question

lcm and hcf 2 cube x 3 square x 5 and 3 cube x 5 square x 2 cube?

Answer 1

Hcf

Take only common terms2x2x2x3x3x5=360

Lcm

2x2x2x3x3x5,3x3x3x5x5x2x2x2

Take maximum power terms=3x3x3x5x5x2x2x2=5400

Answer 2

The L.C.M of $(2)^{3} \times(3)^{2} \times 5\ \text{and}\ (3)^{3} \times(5)^{2} \times(2)^{3}$ is 5400  

The H.C.F of  $(2)^{3} \times(3)^{2} \times 5\ \text{and}\ (3)^{3} \times(5)^{2} \times(2)^{3}$is 360

Given:

The two terms are $(2)^{3} \times(3)^{2} \times 5\ \text{and}\ (3)^{3} \times(5)^{2} \times(2)^{3}$

To find:

The L.C.M and H.C.F

Solution:

First term = 2 cube × 3 square × 5 = (2)^{3} \times(3)^{2} \times 5

Second term $=3 \text { cube } \times 5 \text { square } \times 2 \text { cube }= (3)^{3} \times(5)^{2} \times(2)^{3}$

Now to find LCM, we have to take maximum powers of factors of both terms.

So, LCM $= (2)^{3} \times(3)^{3} \times(5)^{2}$

$\begin{array}{l}{=(2 \times 2 \times 2) \times(3 \times 3 \times 3) \times(5 \times 5)} \\ {=8 \times 27 \times 25} \\ {=5400}\end{array}$

Now to find HCF, we have to take only common powers of factors of both terms.

So, HCF $= (2)^{3} \times(3)^{2} \times(5)$

$\begin{array}{l}{=(2 \times 2 \times 2) \times(3 \times 3) \times(5)} \\ {=8 \times 9 \times 5} \\ {=360}\end{array}$

Hence LCM = 5400, HCF = 360