Primes, HCF and LCM - Highest Common Factor and Its Applications

Find the highest common factor and lowest common multiple of the following

1. \(5^2 \times 7^4 \times 11^3 \times 13^2 \times 17\), \(2^5 \times 3^2 \times 5^2 \times 7\) and \(2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17\)
2. \(2^3 \times 5^2 \times 7 \times 13 \times 17^2\), \(3^4 \times 5^2 \times 11^2 \times 13^2 \times 17\) and \(9750\)
3. \(780\), \(1350\) and \(3510\)

leaving your answer in index notation.