Question

The product of two numbers is $6912$ and their GCD is $24 $. What is their LCM?

Answer 1

Hint: from the question given that the product of two numbers is $6912$and their GCD is $24$, now we have to find the LCM of those two numbers. As we know that the if “a” and “b” are two numbers then the product of these two numbers will be equal to the product of the GCD and LCM of the “a”, “b” that is $GCD\left( a,b \right)\times LCM\left( a,b \right)=product\left( a,b \right)=a\times b$. From this relation we will get the LCM of the two numbers.

Complete step by step solution:
From the question given that the product of two number is
$\Rightarrow product=6912$
And the GCD of two numbers is
$\Rightarrow GCD=24$
Now we can find the LCM by known relation that is we know that the if “a” and “b” are two numbers then the product of these two numbers will be equal to the product of the GCD and LCM of the “a”, “b” that is
$\Rightarrow GCD\left( a,b \right)\times LCM\left( a,b \right)=product\left( a,b \right)=a\times b$
From this relation we will get the LCM,
Now we have to substitute the values in their respective positions in the relation above,
By substituting the values, we will get,
$\Rightarrow GCD\left( a,b \right)\times LCM\left( a,b \right)=product\left( a,b \right)=a\times b$
$\Rightarrow 24\times LCM=6912$
Now by simplifying further we will get,
$\Rightarrow LCM=\dfrac{6912}{24}$
By further simplifying we will get,
$\Rightarrow LCM=288$

Therefore, the required LCM is $288$.

Note: Students should know the relation between LCM, GCD and product of the two numbers. Students should also know how to find GCD and LCM if two or more numbers are given. GCD means greatest common divisor and LCM means least common multiple.