If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is
Let the HCF be x and the LCM of the two numbers be y. It is given that the sum of the HCF and LCM is 1260 x + y = 1260 …… (i) And, LCM is 900 more than HCF. y = x + 900 …… (ii) Substituting (ii) in (i), we get: `x + x + 900 = 1200` `2x +900=1260` `2x = 1260 -900` `2x = 360` x = 180 Substituting x = 180 in (ii), we get: y = 180 + 900 y = 1080 We also know that the product the two numbers is equal to the product of their LCM and HCF Thus the product of the numbers = 194400(180) = 194400 Hence, the correct choice is (b). Concept: Euclid’s Division Lemma Is there an error in this question or solution? Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now
10 Questions 10 Marks 10 Mins
Given: The ratio of two numbers = 5 ∶ 9 LCM = 765 Concept Used: The product of two numbers = LCM × HCF Calculation: Let the two numbers be 5x and 9x According to the question, we have The LCM of 5x and 9x = 5 × 9 × x ⇒ 45x Now, the LCM of two numbers is 45x = 765 ⇒ x = 765/45 ⇒ x = 17 The first number = 5x ⇒ 5 × 17 ⇒ 85 The second number = 9x ⇒ 9 × 17 ⇒ 153 ∴ The two numbers are 85 and 153. India’s #1 Learning Platform Start Complete Exam Preparation
Daily Live MasterClasses
Practice Question Bank
Mock Tests & Quizzes Trusted by 3.3 Crore+ Students |