What is the LCM of the numbers 3, a, and 7, if 'a' is an integer and a ≥ 3?
Statement 1. 'a' is a prime number greater than 2.
Statement 2. Both GCD (3, a) and LCM (3, a) are factors of the number 30.
OA E
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What is the LCM of the numbers 3, a, and 7, if ‘a’ is an
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Statement 1 is not sufficient, because the LCM will be different if a=5 or if a=97.
For Statement 2, the GCD of 3 and anything must be a divisor of 3, so it could only be 1 or 3, and will always be a divisor of 30. So Statement 1 only tells us "the LCM of 3 and a is a divisor of 30". That will be true if a is 3 or 5 (among other possibilities), and we get a different answer to the original question using a=3 and a=5. Since 3 and 5 are both prime numbers, we've just used both Statements together, so the answer is E.
For Statement 2, the GCD of 3 and anything must be a divisor of 3, so it could only be 1 or 3, and will always be a divisor of 30. So Statement 1 only tells us "the LCM of 3 and a is a divisor of 30". That will be true if a is 3 or 5 (among other possibilities), and we get a different answer to the original question using a=3 and a=5. Since 3 and 5 are both prime numbers, we've just used both Statements together, so the answer is E.
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