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### Grade 6 - Mathematics1.43 Relation Between G.C.D. and L.C.M.

 The greatest common divisor (GCF) of two positive whole numbers is the product of the prime factors common to both numbers. The least common multiple (LCM) is the smallest multiple common to both numbers. Sometimes these terms are written as greatest common divisor GCD, and lowest common denominator LCD, when they are being used with fractions. Relationship between G.C.D and L.C.M. through an example: Example: Consider the numbers 8 and 12. Let us find the L.C.M. of 8 and 12. 8 = 2 x 2 x 2 12 = 2 x 2 x 3 Collect the largest number of occurrence of each prime number. The largest number of times the factor 2 occurs is three. The largest number of times the factor 3 occurs is one. Therefore the L.C.M. is = 2 x 2 x 2 x 3 = 24. Now let us find the G.C.D. of 8 and 12. 8 = 2 x 2 x 2 12 = 2 x 2 x 3 We observe that 2, 2 are the common prime factors of 8 and 12. Hence the G.C.D. of 8 and 12 is = 2 x 2 = 4. Now, we find the product of G.C.D. and L.C.M., that is LCM x GCD = 24 x 4 = 96. Now we shall find the product of two given numbers. i.e., 1st number x 2nd number = 8 x 12 = 96. From the above example, we find that 1st number x 2nd number = LCM x GCD. Hence, the product of two numbers is equal to the product of LCM and GCD of the two numbers. On the basis of this relation, we find that: 1st number = (LCM x GCD)/ 2nd number 2nd number = (LCM x GCD)/ 1st number LCM = (1st number x 2nd number)/ GCD GCD = (1st number x 2nd number)/ LCM Directions:Answer the following questions. Also write at least 10 examples of your own.
 Q 1: The GCD and LCM of two numbers are 250 and 14700 respectively. If one of the numbers is 5250, what is the other number?500700600 Q 2: The GCD of two numbers is 9 and their LCM is 54, if one of the number is 18, find the other.273747 Q 3: The GCD of two numbers is 3 and their LCM is 150. If one of the number is 15, what is the other number?504030 Q 4: The GCD and LCM of two numbers are 25 and 1750 respectively, if one of the number is 175, find the other.150350250 Q 5: The product of two numbers is 3276. If their GCD is 6, find their LCM.546450500 Q 6: Find the LCM of the two numbers, if their product is 140 and GCD is 2?705060 Q 7: If LCM of two numbers is 290 and their product is 7250, what will be its GCD?352530 Q 8: The LCM of 60 and 75 is 300, find their GCD.153525 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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