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What is the relation between the HCF and the LCM of numbers?
LCM
is the lowest common multiple of given numbers. The multiples of the numbers are found. Then the common multiples of the given numbers are considered. The lowest of these common multiples is the LCM of the numbers.
HCF
is the highest common factor of given numbers. The prime factors of the numbers are found and then the common factors are found and the highest among those factors is found and that is the HCF of those numbers.
The product of LCM and HCF of the given natural numbers is equivalent to the product of the given numbers
Product of Numbers = HCF $\times$ LCM.
This is the relation between the HCF and LCM of the numbers.
Example: 18, 48
18 = 2 $\times$ 3 $\times$ 3; 48 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3
The LCM = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 = 144;
HCF = 2 $\times$ 3 = 6
LCM of 18 and 48 is 144. HCF of 18 and 48 is 6
Product of the numbers =18 $\times$ 48 = HCF $\times$ LCM = 6 $\times$ 144
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