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.
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