7. identify the gcf and lcm of each pair of numbers.\na) 78 = 2×3×13\n442 = 2×13×17\nb) 32 = 2×2×2×2×2\n24 =…

7. identify the gcf and lcm of each pair of numbers.\na) 78 = 2×3×13\n442 = 2×13×17\nb) 32 = 2×2×2×2×2\n24 = 2×2×2×3

7. identify the gcf and lcm of each pair of numbers.\na) 78 = 2×3×13\n442 = 2×13×17\nb) 32 = 2×2×2×2×2\n24 = 2×2×2×3

Answer

Explanation:

Step1: Find GCF for a)

The common factors of 78 and 442 are 2 and 13. So GCF = $2\times13=26$.

Step2: Find LCM for a)

LCM is found by taking the highest - power of each prime factor involved. So LCM=$2\times3\times13\times17 = 1326$.

Step3: Find GCF for b)

The common factors of 32 and 24 are three 2s. So GCF = $2\times2\times2 = 8$.

Step4: Find LCM for b)

For 32 and 24, LCM=$2\times2\times2\times2\times2\times3=96$.

Answer:

a) GCF = 26, LCM = 1326 b) GCF = 8, LCM = 96