If 49392 = a4b2c3, find the values

Question:

If $49392=a^{4} b^{2} c^{3}$, find the values of $a$, $b$ and $c$, where $a, b$ and $c$, where $a, b$, and $c$ are different positive primes.

Solution:

Taking out the LCM, the factors are $2^{4}, 3^{2}$ and $7^{3} a^{4} b^{2} c^{3}=2^{4}, 3^{2}$ and $7^{3}$

$a=2, b=3$ and $c=7$ [Since, $a, b$ and $c$ are primes $]$

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