16x7=112 so 112 is a multiple of 7
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Oh, dude, the LCM of 7, 14, and 16 is 112. It's like the smallest multiple that all three numbers can divide into evenly. So, if you're throwing a party for 7, 14, and 16 people, you better have at least 112 cupcakes to share.
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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7 times 16 = 112
The square root of 112 simplified is √112 = 4√7. Here's how you can break it down: First, find the prime factorization of 112: 112 = 2^4 * 7. Take the square root of each of the factors: √(2^4 * 7) = √(2^4) * √7 = 2^2 * √7 = 4√7. So, the simplified radical form of √112 is 4√7.