Question

How do you find the LCM of \[15,20\].

Answer 1

Hint: LCM is basically called the least common multiple. This method is basically used to find the smallest common multiple between any of two or more numbers. So, to find LCM firstly we will try to find the prime factorization of both numbers, and then we will multiply each factor the greater number of times it occurs to find the LCM. prime factorization is basically a method in which we break down a number into a set of prime numbers which when multiplied results in the original number.

Complete step by step solution:
Firstly we will write prime factors of both numbers that is \[15,20\]
Prime factorization of \[15 = 3 \times 5\]
Prime factorization of \[20 = 2 \times 2 \times 5\]
Now, we will multiply each factor the greater number of times it occur that is
 \[\begin{array}{c}
LCM{\rm{ }}\,of\,{\rm{ }}(15,20) = 2 \times 2 \times 3 \times 5\\
 = 60
\end{array}\]

So, our answer is \[60\].

Note: We must write only prime factors of numbers. We can find \[LCM{\rm{ }}\,of\,{\rm{ }}\,n\] numbers but The value of n should be greater than or \[equal\,to\,2\]. We need to take care while multiplying each factor the greater the number of times it occurs. We can find L.C.M (least common multiple) of only rational numbers. L.C.M (least common multiple) of any irrational is not possible. Therefore the numbers must be of rational number type.