Question

What‌ ‌is‌ ‌the‌ ‌least‌ ‌common‌ ‌multiple‌ ‌of‌ ‌12,‌ ‌18‌ ‌and‌ ‌5?‌

Answer 1

Hint: The‌ ‌least‌ ‌common‌ ‌multiple‌ ‌of‌ ‌any‌ ‌amount‌ ‌of‌ ‌numbers‌ ‌is‌ ‌the‌ ‌least‌ ‌number‌ ‌that‌ ‌is‌ ‌the‌ ‌common‌ ‌multiple‌ ‌of‌ ‌all‌ ‌the‌ ‌numbers‌ ‌given.‌ ‌For‌ ‌this,‌ ‌we‌ ‌just‌ ‌simply‌ ‌find‌ ‌the‌ ‌multiples‌ ‌of‌ ‌the‌ ‌numbers‌ ‌given‌ ‌and‌ ‌then‌ ‌we‌ ‌find‌ ‌the‌ ‌common‌ ‌multiples‌ ‌of‌ ‌them.‌ ‌After‌ ‌that‌ ‌we‌ ‌pick‌ ‌the‌ ‌least‌ ‌one‌ ‌out‌ ‌of‌ ‌them‌ ‌which‌ ‌will‌ ‌be‌ ‌ the‌ ‌least‌ ‌common‌ ‌multiple‌ ‌of‌ ‌the‌ ‌numbers‌ ‌given.‌ ‌But‌ ‌if‌ ‌the‌ ‌numbers‌ ‌are‌ ‌a‌ ‌bit‌ ‌large‌ ‌then‌ ‌we‌ ‌can‌ ‌do‌ ‌factorization‌ ‌of‌ ‌the‌ ‌numbers‌ ‌and‌ ‌then‌ ‌find‌ ‌the‌ ‌minimum‌ ‌number‌ ‌that‌ ‌includes‌ ‌all‌ ‌the‌ ‌factors.‌ ‌

Complete step-by-step solution:
We have the number 12, 18 and 5:
We begin by writing the prime factorization of 12:
$12=2\times 2\times 3$
Now, we write the prime factorization of 18:
$18=3\times 3\times 2$
And lastly, we write the prime factorization of 5:
$5=5\times 1$
After, the prime factors have been written for each number, we see that the number $2\times 2\times 3\times 3\times 5$ and the number obtained by multiplying these terms is 180:
$2\times 2\times 3\times 3\times 5=180$
So, the least common multiple of 12, 18 and 5 is 180.

Note: Do not try to write the multiples of the numbers given to find the least common one out, because that might take a large amount of time since the numbers are large. If you are not able to find any common multiples up to a certain limit then simply do the factorization and create the number which is the least and which has all the factors. Here, even if you write the multiples of 12 up to 120, you still won’t be able to find any common factor and then you will have to find the further factors of it which will require a lot of time.