Quiz-1 Day-1

If GCD(a, b) = d, then which of the following is always true?

• a/d and b/d are co-prime

• LCM(a, b) = (a × b) / d

• a × b = GCD(a, b) × LCM(a, b)

• All of the above

The product of two numbers is 693. Their GCD is 11. What is their LCM?

• 21

• 33

• 63

• 693/11

A number leaves remainder 1 when divided by 2, 3, and 4. What is the smallest such number?

• 13

• 25

• 37

• 49

If p and q are distinct prime numbers, then GCD(pq, p+q) is:

• p

• q

• 1

• p+q

Which of the following statements about prime numbers is false?

• Except 2, all prime numbers are odd.

•  Every prime greater than 3 can be written in the form 6k ± 1.

• There are infinitely many primes of the form 4k + 1.
  

• Every even number greater than 2 is prime.

If LCM(a, b) = 180 and GCD(a, b) = 6, and a = 18, what is b?

• 30

• 36

• 60

• 90

The largest 3-digit number divisible by both 9 and 15 is:

• 945

• 990

• 975

• 999

If the sum of two numbers is 84 and their GCD is 12, then what is the maximum possible LCM of the two numbers?

• 252

• 144

• 420

• 504

Which of the following is true about prime numbers?

• There are infinitely many primes of the form 2n + 1.

• There are infinitely many primes of the form 4n + 3.

• Twin primes are consecutive prime numbers.

• Goldbach’s conjecture has been proven true.