Final answer:
The least common multiple of a^3 b^5 c^7 and a^7 b^2 c is a^7 b^5 c^7, obtained by taking the highest exponents for each base from the given expressions.
Step-by-step explanation:
To find the least common multiple (LCM) of a3 b5 c7 and a7 b2 c,
we analyze each base and use the highest power of the base that appears in any of the expressions.
For the base a, the highest exponent is 7 from a7.
For the base b, the highest exponent is 5 from b5. And for the base c, the highest exponent is 7 from c7.
Combining these, we get the LCM as a7 b5 c7.