Question

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

Answer 1

Answer:

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