Find the LCM of this
6^4c^9, 3a^3c^7, 14a^8c^7
correction:
6a^4c^9, 3a^c^7,14a^8c^9
Find the LCM of this
6a^4c^9, 3a^3c^7, 14a^8c^7
To find the least common multiple (LCM) of the given expressions, follow these steps:
Step 1: Split each expression into its prime factors:
6^4c^9 = (2^2 * 3^1)^4 * c^9
3a^3c^7 = 3^1 * a^3 * c^7
14a^8c^7 = (2^1 * 7^1) * a^8 * c^7
Step 2: Identify the highest power of each prime factor that appears in any of the expressions. Take the maximum exponent for each prime factor:
For 2: the highest power is 2^2
For 3: the highest power is 3^1
For 7: the highest power is 7^1
For a: the highest power is a^8
For c: the highest power is c^9
Step 3: Multiply all the identified highest powers together:
LCM = 2^2 * 3^1 * 7^1 * a^8 * c^9
Therefore, the LCM of the given expressions is 84a^8c^9.