LCM
Factor: one number is said to be a factor when it divides the other number exactly. Thus 2 and 3 are factors of 6.
Multiple: one number is said to be a multiple of other number when it is exactly divisible by the other.
Common factor: A common factor of two or more numbers is a number that divides each of them exactly. Thus 8 is a common factor 16,24,66 and 96.
Common multiple: A common multiple of two or more numbers Ma number which is exactly divisible by each of them. Thus 24 is n common multiple of 2, 3,4,6,8 and 12.
Least Common Multiple (LCM): The least number, which is exactly divisible by two or more given numbers.
Method to find LCM
Method of prime factors: Divide the given numbers into their prime factors and then find the product film highest power dell the factors that occur in the given numbers, and this product will be the required LCM.
Example: LCM of 4, 8 and 24 is
4 = 2 x 2 =2²
8 = 2 x 2 x 2 = 2³
24 = 2 x 2 x 2 x 3 = 2³ x 3
The prime factors that occur here are 2 and 3. The highest powers of these prime factors are 2³ and 3¹ respectively.
Therefore the required LCM is 2³ x 3¹ = 24
Regular method: Write all the given numbers M a line and divide them by a number which will exactly divide atleast any two of the numbers. Write down the quotient, and the undivided numbers in a line below the first.Repeat the process until weed a line of numbers which are prime to each other. The product of all the divisors and the numbers in the lest hue wall be the required LCM.
Example: LCM of 4,8,12,14 and 32 is
Therefore required LCM is 2 x 2 x 2 x 3 x 7 x 4 =672
LCM of decimals
First find LCM of the given numbers without decimals and then put the decimal in the result after the number of digits which is equal to the minimum digits after the decimal in the given numbers from right to left.
Example: LCM of 2.4,0.012 and 0.32 is
LCM of 24,12 and 32 is 96
In the given numbers the minimum digits from right to left it in 2,4 i.e.,1
Therefore the required LCM is 9.6.
