Subject
Quantitative Aptitude
Topic
LCM & HCF
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
ক)
15খ)
0গ)
2ঘ)
7Explanation
Let the numbers 13a and 13b. Then, 13a x 13b = 2028 =>ab = 12. Now, the co-primes with product 12 are (1, 12) and (3, 4). [Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ] So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4). Clearly, there are 2 such pairs.Related questions
If HCF(a,b) = 12, LCM(a,b) = 420, and a < b, then a + b = ?The H.C.F and L.C.M of two numbers are 11 and 385 respectively. If one number lies between 75 and 125 , then that number isThe HCF of three numbers is 8 and their LCM is 1680. If two of the numbers are 56 and 120, what is the third number?The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:What is the least number when divided by 4,5,6 leaves remainder 3 in each case?If a² - b² = 48 and ab = 140, then what is the HCF(a,b)?The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 isIf 2ⁿ × 3ᵐ × 5ᵖ = 1500, then n + m + p = ?