Question

The LCM of 30 and 45?

Answer 1

Hint: LCM stands for least common multiple. LCM of (a,b), is the smallest positive integer that is divisible by both a and b, where a and b are non-zero numbers. LCM of more than two integers is also defined.

Complete step-by-step answer:
We get a multiple of a number when we multiply it by another number. Common multiples are the multiples which are found in all the numbers whose LCM is to be calculated.
Least common multiple (LCM) is also called as Least Common Divisor (LCD).
LCM is also used to add or subtract two fractions when the denominators of the fractions are different. It is used to make a common denominator.
To find the LCM, factorize the numbers into their prime factors that are multiplied to create the same no.
Prime factorisation of 30 and 45 is given below:-
\[\] $\begin{align}
  & 30=2\times 3\times 5 \\
 & 45=3\times 3\times 5 \\
\end{align}$
To find the LCM, pair the common multiples of both numbers. Common multiples of both the numbers are $3$and$5$.
To find the LCM, product the common multiples along with the remaining multiples.
Remember, the common multiples are written single time in product to find the LCM.
LCM $=2\times 3\times 3\times 5$
 $=90$
Therefore, LCM of 30 and 45 is 90. Which the least common multiple of both the numbers is $90$.
Formula for finding lcm(a,b)=$\dfrac{\left| a\centerdot b \right|}{\gcd (a,b)}$
Where lcm(a,b) represents LCM of integers a and b
gcd(a,b) is greatest common divisor of integers a and b
So, the correct answer is “90”.

Note: You can use various methods to find the LCM of two or more numbers.
The different methods are listed below:-
i.Prime factorisation
ii.Repeated division
iii.Multiples