Properties of LCM And HCF
There are many properties of LCM and HCF :
The product of LCM and HCF of any two given natural numbers is equal to the product of the given numbers.
LCM × HCF = Product of the Numbers
If A and B are two numbers, then.
LCM (A & B) × HCF (A & B) = A × B
The H.C.F. of two or more numbers can not be greater than any one of them.
For example, the H.C.F. of 16, 18 and 24 is 2 which is less than all the given numbers.
If one number is a factor of the other numbers, their H.C.F. will be always that smallest number.
For example, 9 is the H.C.F. of 18, 36 and 45.
Because 18, 36 and 45 is the factor of 9.
HCF of co-prime numbers is always 1.
HCF of Co-prime Numbers = 1
LCM of given co-prime numbers is equal to the product of the numbers.
LCM of Co-prime Numbers = Product Of The Numbers
H.C.F. and L.C.M. of Fractions
LCM of fractions = LCM of numeratorsHCF of denominators
HCF of fractions = HCF of numeratorsLCM of denominators
Example: Find the HCF of 1225, 910, 1835, 2140
Solution: The required HCF is = HCF of 12,9,18,21
LCM of 25,10,35,40 = 31400
The L.C.M. of two or more numbers is not less than any of the given numbers.
LCM of given numbers is a multiple of their HCF.
For example, HCF of 16, 12 = 4
LCM of 16, 12 = 48
LCM 48 is a multiple of HCF 4.
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