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Subject – Mathematics


                                    Chapter 3 – FACTORS AND MULTIPLES

        Sub-topic-8:- Relation between HCF and LCM


                 Facts about HCF and LCM.
                Two numbers are said to be co- prime, if their HCF is 1.
                The LCM of two co- prime numbers is equal to their product.
                If one number is a factor of the other number, then this HCF  is the smaller number and their
                 LCM is the larger number.
                Product of two given numbers is equal to the product of their HCF and LCM.Thus we have :
                HCF x LCM = Product of the given number
                LCM of two given numbers =First number x second number
                                                                HCF of the given numbers

                If HCF and LCM is given and one number is given,how to find the other number.
                 Other number = HCF x LCM
                  Given number
                 Example:-
                 Highest common factor and lowest common multiple of two numbers are 18 and 1782
                 respectively. One number is 162, find the other.
                 Solution:-
                 We know, H.C.F. × L.C.M. = First number × Second number then we get,
                 18 × 1782 = 162 × Second number
                 18 × 1782/162 = Second number
                 Therefore, the second number = 198

                 Example:-
                 The HCF of two numbers is 144 and their Lcm is 2880.If one of the numbers is 720, find the
                 other number.
                 Solution:-
                 HCF =144   , LCM = 2880
                 One number =720
                 Other number = HCF x LCM
                                          Given number

                                  = 144x 2880
                                      720
                                  = 576

                 Hence, the other number is 576
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