H.C.F. & L.C.M.
 Factorization & Division Method
 HCF & LCM of Fractions & Decimal Fractions
Methods
On Basis

H.C.F. or G.C.M

L.C.M.

Factorization Method

Write each number as the product of the prime factors. The product of least powers of common prime factors gives H.C.F. Example: Find the H.C.F. of 108, 288 and 360. 108 = 2^{2}✘3^{3}, 288 = 2^{5}✘32 and 360 = 23✘5✘32
H.C.F. = 22✘32=36 
Write each numbers into a product of prime factors. Then, L.C.M is the product of highest powers of all the factors. Examples: Find the L.C.M. of 72, 108 and 2100. 72=23✘32,108=33✘22, 2100=22✘52✘3✘7. L.C.M.=23✘33✘52✘7=37800 
Division Method

Let we have two numbers .Pick the smaller one and divide it by the larger one. After that divide the divisor with the remainder. This process of dividing the preceding number by the remainder will repeated until we got the zero as remainder.The last divisor is the required H.C.F. H.C.F. of given numbers = 69

Let we have set of numbers.
First of all find the number which divide at least two of the number in a given set of number.remainder and not divisible numbers will carry forward as it is. Repeat the process till at least two number is not divisible by any number except 1.The product of the divisor and the undivided numbers is the required L.C.M. Example: 
H.C.F. & L.C.M. of Fractions

H.C.F. = ^{H.C.F. of Numerator }/_{ L.C.M. of Denominators}  L.C.M. = ^{L.C.M. of Numerator }/_{ H.C.F. of Denominators} 
Product of H.C.F. & L.C.M. 
H.C.F * L.C.M. = product of two numbers


Decimal numbers  H.C.F. of Decimal numbers Step 1. Find the HCF of the given numbers without decimal. Step 2.Put the decimal point ( in the HCF of Step 1) from right to left according to the MAXIMUM deciaml places among the given numbers. 
L.C.M. of Decimal numbers Step 1. Find the LCM of the given numbers without decimal. Step 2.Put the decimal point ( in the LCM of Step 1) from right to left according to the MINIMUM deciaml places among the given numbers. 