Relationship Between HCF & LCM


Earlier, we learnt about  and ..Today we will look at a few relationships between these numbers.

$\underline{Relationship\ Between\ The\ Numbers\ And\ Their\ HCF\ \&\ LCM}$
For any $two$ numbers, if we take the product of the numbers and the product of their $HCF$ and $LCM$, they are always equal.
For example the $HCF$ of $18$ and $12$ is $6$, and their $LCM$ is $36$.

The product of the two numbers, in this case is $18 \times 12 =  216$
The product of their LCM and HCF is $6 \times 36 = 216$
And we can see that they are the same.

However, this is not necessarily true for $three\ or\ more$ given numbers.

$\underline{Relationship\ Between\ HCF\ \&\ LCM}$ 
The LCM of two or more numbers is a multiple of all the given numbers and it is divisible by all the given number and all their factors as well.
The HCF is a factor of all the given numbers. Therefore, the LCM of two or more number is always divisible by the HCF of the given numbers.