(c) Two large numbers are writte \( 2^{10} \times 3^{15} \times 5^{20} \times 7 \) \( 2^{15} \times 3^{10} \times 5^{20} \times 11 \) Write down the LCM of thes

To find the least common multiple (LCM) of the two numbers \( 2^{10} \times 3^{15} \times 5^{20} \times 7 \) and \( 2^{15} \times 3^{10} \times 5^{20} \times 11 \), we take the highest power of each prime factor present in either number. - For \(2\), the maximum power is \(2^{15}\). - For \(3\), the maximum power is \(3^{15}\). - For \(5\), the maximum power is \(5^{20}\). - For \(7\), it's \(7^{1}\) (only present in the first number). - For \(11\), it's \(11^{1}\) (only present in the second number). Combining these, the LCM is: \[ LCM = 2^{15} \times 3^{15} \times 5^{20} \times 7^1 \times 11^1 \] This expression captures the essence of both numbers while ensuring that all prime factors are included at their highest powers!