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Highest Common Factor (HCF):

Consider the numbers 12 and 15:
12= 1×2×2×3
1 and 3 are the only common factors (numbers which are factors of both 12 and 15).
Therefore, the highest common factor of 12 and 15 is 3.
The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers.
In other words the H.C.F is the largest of all the common factors.

Least Common Factor (LCM):

Consider the number 924 & 240
924 = 2 x 3 x 7 x 11
240 = 
2 x 2 x 2 x 3 x 5  
The L.C.M. is 2 x 2 x 3 x 7 x 11 x 2 x 2 x 5 = 924 x 20 = 18,480 

Hence the LCM is the least number which is exactly divisible by each one of the given number.

Points to Remember:
LCM HCF= Product of Two numbers

H.C.F & L.C.M. of Fractions:

·       H.C.F. = HCF of Numerator/ LCM of Denominator
·       L.C.M. = LCM of Numerator/ HCF of Denominator

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