If $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then…

Question

If $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{	ext{LCM}(a,b)}{	ext{HCF}(a,b)}$ equals

Accepted Answer

C. $2 \cdot 3^2 \cdot 5^2 \cdot 7$

**HCF takes min powers:** $2^3 3^2$.
**LCM takes max powers:** $2^4 3^4 5^2 7$.
Ratio $= 2^{4-3} 3^{4-2} 5^2 7 = 2\cdot3^2\cdot5^2\cdot7$.

Answer

$2^7 \cdot 3^6 \cdot 5^2 \cdot 7$

Answer

$2 \cdot 3^2 \cdot 5 \cdot 7$

Answer

$2^4 \cdot 3^4 \cdot 5^2 \cdot 7$

If $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(a,b)}{\text{HCF}(a,b)}$ equals