Simplification ( Part III)

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 = 22✘33, 288 = 25✘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. Example: 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: Find the L.C.M. of 12,36,48,72
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

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