### what is LCM?

The Least Common multiple of two or more given numbers is the least or lowest number which is exactly divisible by each of them.

**Example :**Find the LCM of 36, 56, 105 & 108.

**Solution:**36 = 2*2*3*3

56 = 2*2*2*7

105 = 3*5*7

108 = 2*2*3*3*3

Now take all the number with heighest power :

**LCM :**2^3*3^3*5*7 = 7560

### what is HCF?

HCF of two or more numbers is the greatest number which divides each of them exactly.

HCF is also known as Highest Common Divisor(HCD) and Greatest Common Measure(GCM).

**Example :**Find the HCF of 36, 42 & 126.

**Solution:**36 = 2*2*3*3

42 = 2*3*7

126 = 2*3*3*7

Now take the common number with lowest power :

**HCF :**2*3

**Important Formulas**

**1).**Relation between the two numbers and their HCF and LCM is :

HCF * LCM = first Number * Second Number

**2).**HCF of fraction = HCF of Numerators/ LCM of Denominators

**3).**LCM of Fraction = LCM of Numerators/HCF of Denominators

**Example :**The LCM of 4/45, 6/15 and 12/21 is ?

**Solution :**LCM = LCM of Numerators/HCF of Denominators

= LCM of 4,6 and 12/HCF of 45, 15 and 21

= 12/3

= 4

### Average

**What is Average?**

The average of a give observation or data is a number which is found on dividing the sum of observations or data by the number of observation or data given.

Average = Sum of observations/Number of observations

**Example :**Find average of 3,7,9 & 13.

**Solution :**3+7+9+13/4

= 32/4

= 8.

**Important Formulas**

**)1.**Average of first 'n' natral numbers = (n+1)/2

**2).**Average of first 'n' even numbers = (n+1)

**3).**Average of first 'n' odd numbers = n

**4).**Average of consecutive numbers = (First Number + Last Number)/2

**5).**Average of '1 to n' odd numbers = (Last odd number +1)/2

**6).**Average of '1 to n' even numbers = (Last even number +2)/2

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