Question
Two numbers have LCM 360 and HCF 12. If one of the numbers is 72, find the other number. Also find how many common divisors the two numbers have.
Solution
For two numbers a and b: a × b = LCM × HCF Let other number be x. 72 × x = 360 × 12 72x = 4320 ⇒ x = 4320 / 72 = 60 Other number = 60. Common divisors of the two numbers are the divisors of their HCF = 12. Prime factorization of 12 = 2² × 3¹ Number of divisors = (2 + 1)(1 + 1) = 3 × 2 = 6 So they have 6 common divisors.
More HCF and LCM Questions
- Find the HCF of 864 and 582.
- What is the HCF of 36 and 198?
- The HCF of two numbers is 12 and their LCM is 420. If one number is 84, find the other number.
- Three boys runs around a circular track and takes 24 min, 40 min and 42 min respectively to complete the one round. When do they all come relatively to the...
- The least multiple of 19, which on dividing by 5,6,7,8 and 9 leaves remainder 2 in each case is
- Find the greatest number which when divide 28, 82 & 109 leave a same remainder 1 in each case?
- The ratio of two numbers is 4:8 and their LCM is 96. The numbers are:
- What is the difference between the LCM and HCF of 35, 40?
- In a class, the ratio of number of boys to number of girls is 8:5. If 1 boy joined the class and 2 girls left the class, then the ratio becomes 7:4. Find t...
- Find the HCF of two numbers if LCM and product of those two numbers are 65 and 975 respectively.
