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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 6 - Mathematics
1.45 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 product of two numbers is 3276. If their GCD is 6, find their LCM.
546
500
450

 Q 2: The GCD and LCM of two numbers are 250 and 14700 respectively. If one of the numbers is 5250, what is the other number?
600
500
700

Q 3: The product of two numbers is 360. Find their LCM if their GCD is 3.
150
100
120

 Q 4: Find the LCM of the two numbers, if their product is 140 and GCD is 2?
60
50
70

Q 5: The LCM of 60 and 75 is 300, find their GCD.
15
25
35

 Q 6: The GCD and LCM of two numbers are 25 and 1750 respectively, if one of the number is 175, find the other.
250
350
150

Q 7: The GCD of two numbers is 3 and their LCM is 150. If one of the number is 15, what is the other number?
50
30
40

 Q 8: The GCD of two numbers is 9 and their LCM is 54, if one of the number is 18, find the other.
37
27
47

Question 9: This question is available to subscribers only!

 Question 10: This question is available to subscribers only!


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