Question

Find the LCM and HCF of p and q where p=a3b
2 and q= b3a
2​

Answer 1

AnsWer :

• HCF = ( a² , b² )
• LCM = ( a³ , b³ )

Solution :

We have,

• P = a³ b²
• q = a² b³

# For H.C.F ( Highest Common factor )

$\tt (p , q ) = {a}^{3} {b}^{2} \: , \: {a}^{2} {b}^{3}$

$\tt p \leadsto a \times a \times a \times b \times b.$

$\tt q \leadsto a \times a \times b \times b \times b.$

Taking Common factor in both ( p , q )

$\tt \dagger \: \: \: \: \:H.C.F (p , q) \leadsto {a}^{2} \: {b}^{2} .$

$\rule{120}1$

# For L.C.M ( Least common multiple )

$\tt (p \: q ) = {a}^{3} {b}^{2} \: ,\: {a}^{2} {b}^{3}$

$\tt p \leadsto a \times a \times a \times b \times b.$

$\tt q \leadsto a \times a \times b \times b \times b.$

Taking highest degree in both ( p , q )

$\tt \dagger \: \: \: \: \: L.C.M (p , q) \leadsto {a}^{3} \: {b}^{3} .$

Therefore, HCF of given value be a² b² and LCM of given value be a³ b³.

Answer 2

LCM and HCF

To find LCM and HCF, simply express the given terms as a product $\mathsf{a}$ and $\mathsf{b}$.

Here, $\mathsf{p=a^{3}b^{2}}$

$\Rightarrow \mathsf{p=a\times a\times a\times b\times b}$

and $\mathsf{q=b^{3}a^{2}}$

$\Rightarrow \mathsf{q=b\times b\times b\times a\times a}$

Finding HCF.

We see that, in $\mathsf{p}$ and $\mathsf{q}$, there are two $\mathsf{a}$ and two $\mathsf{b}$ are common.

Thus HCF of $\mathsf{p,\:q=a\times a\times b\times b}$

$\quad\quad=\mathsf{a^{2}b^{2}}$

$\Rightarrow \boxed{\mathsf{HCF(p,\:q)=a^{2}b^{2}}}$

Finding LCM.

We see that, together in $\mathsf{p}$ and $\mathsf{q}$, there are maximum number of three $\mathsf{a}$ and three $\mathsf{b}$.

Thus LCM of $\mathsf{p,\:q=a\times a\times a\times b\times b\times b}$

$\quad\quad=\mathsf{a^{3}b^{3}}$

$\Rightarrow \boxed{\mathsf{LCM(p,\:q)=a^{3}b^{3}}}$