Find the GCF and LCM of 217x328x11 and 213x345x74and explain your reasoning.

Given expressions are,

217 x 328 x 11

213 x 345 x 74,

Since, 217 = 7 * 31

328 = 2 * 2 * 2 * 41,

11 = 1 * 11,

So, we can write, 217 x 328 x 11 = 7 * 31 * 2 * 2 * 2 * 41 * 1 * 11

Now, 213 = 3 * 71

345 = 3 * 5 * 23,

74 = 2 * 37,

So, 213 x 345 x 74 = 3 * 71 * 3 * 5 * 23 * 3 * 5 * 23

Thus, GCF (greatest common factor) of the given expressions = 1 (because there are no common factors)

We know that if two numbers have GCF 1 then their LCM is obtained by multiplying them,

Hence, LCM (least common multiple) of the given expressions = 217 x 328 x 11 x 213 x 345 x 74