Question

If the \[L.C.M\] of $(54,336) = 3024$, then \[H.C.F\] of $(54,336)$ is

Answer 1

Hint: LCM is the least common multiple. That means, it is the least number that is divisible by both the given numbers. And HCF is the highest common factor. That means, it is the highest number that can divide both the given numbers. You can use the concept that the product of the given number is the product of LCM and HCF.

Complete Step by Step Solution:
It is given that \[L.C.M\] of $(54,336) = 3024$
Hence, the given numbers are, $54$ and $336.$
$H.C.F$ of $(54,336) = ?$
We can use the property that the product of the two given numbers is the product of LCM and HCF. i.e.
Product of two numbers$ = L.C.M$ of numbers $ \times $$H.C.F$ of numbers.
By putting the given value in a formula we can easily get the required answer.
So, put values in formula.
Product of two numbers =$L.C.M\times H.C.F.$
$ \Rightarrow 54 \times 336 = 3024 \times H.C.F$
By rearranging, we can write,
$H.C.F = \dfrac{{54 \times 336}}{{3024}}$
$ \Rightarrow H.C.F = 6$

Hence,$H.C.F$ of $(54,336) = 6.$

Additional information:
LCM is the least common multiple. That means, it is the least number that can be divided by the given numbers.
HCF is the highest common factor. That means, it is the highest number that can divide the given numbers.
HCF is also called gcd (greatest common divisor) in some books.

Note:
Knowing the formula that we have used in this question is good. But even if we didn’t know the formula, we could still calculate the HCF by just factoring both the given numbers into their prime factors and then writing the multiplication of the common factors in both the numbers as the HCF of the two numbers.