Since 16 is a multiple of 8, we can ignore 8 when determining the least common multiple of 14, 8, and 16. The prime factors of 14 are 2 and 7. The prime factors of 16 are 2, 2, 2, and 2. So the least common multiple needs 2, 2, 2, and 2 from 16. Since we already have a 2, we only need the 7 from 14. The least common multiple is 2 x 2 x 2 x 2 x 7 = 112.
Doublecheck:
112 / 14 = 8
112 / 16 = 7
112 / 8 = 14
Since 8 and 7 (the results of dividing by 14 and 16) are relatively prime, this is the least common multiple.
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