Multiple choice

The LCM and HCF of two numbers are 1530 and 51. Find how many such pairs are possible.

  1. $2$
  2. $3$
  3. $4$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

LCM = 1530, HCF = 51. Numbers are 51a and 51b where a, b are coprime. 51a * 51b / 51 = 1530 => 51ab = 1530 => ab = 30. Pairs (a,b) such that gcd(a,b)=1: (1,30), (2,15), (3,10), (5,6). There are 4 pairs.

AI explanation

Let the numbers be 51a and 51b, where a and b are coprime. The LCM is 51ab = 1530, so ab = 30. The coprime pairs for 30 are (1, 30), (2, 15), (3, 10) and (5, 6). There are 4 such pairs possible.

Keep practicing — related questions