Question

Find LCM of $18$ and $27$
A.$44$
B.$54$
C.$34$
D.$24$

Answer 1

Hint: We can find the LCM (lowest common multiple) by using prime factorization method. First find the prime factors of $18$ and $27$ respectively. Factors are the numbers which can divide the given number completely (no remainder is left). Then find the common factors from the given factors of $18$ and $27$. Find the smallest number from the common factors and you’ll have the least common multiple.

Complete step-by-step answer:
Here, given numbers are $18$ and $27$.
We have to find the LCM (lowest common multiple) of these numbers.
We can use factorization methods to find the LCM of these numbers.
First let us find the factors of both the numbers-
Factors are the numbers which can divide the given number completely (no remainder is left).
Now we know that$18 = 2 \times 9$. We can further write it as- $18 = 2 \times 3 \times 3$
Now we can write$27 = 3 \times 9$ . We can further write it as- $27 = 3 \times 3 \times 3$
 So we can write-
Factors of $18 = 2 \times 3 \times 3$ and Factors of $27 = 3 \times 3 \times 3$
So here we can see that $2 \times 3$ and $3 \times 3$ are the common factors of $18$ and $27$.
Now multiply the common factors to find the least common multiple-
LCM=$2 \times 3 \times 3 \times 3 = 54$
So we can say that the Lowest common multiple of these numbers is $54$.

Note: We can also find LCM by using formula –
The product of numbers=HCF× LCM-- (i)
We can find HCF by using the prime factorization method too. First let us find the factors of both the numbers-
Factors of $18 = 2 \times 3 \times 3$ and Factors of $27 = 3 \times 3 \times 3$
Then the highest factors are$3$ and$3$. On multiplying them we get,
HCF=$3 \times 3 = 9$
On substituting the value of HCF and given numbers we get,
$ \Rightarrow 18 \times 27 = 9 \times {\text{LCM}}$
On solving we get,
$ \Rightarrow {\text{LCM}} = 2 \times 27 = 54$