Question

What is the least common multiple of \[15\] and \[50\].

Answer 1

Hint: There are various methods for finding the least common multiple of two given numbers \[15\] and \[50\]. The simplest method to find the least common multiple is by prime factorization method. In the prime factorization method, we first represent the given two numbers as a product of their prime factors and then find the product of all the factors counting the common factors only once.

Complete step by step answer:
To find the least common multiple of \[15\] and \[50\], first we find out the prime factors of both the numbers.
Prime factors of \[15\]$ = 3 \times 5$
Expressing as exponents, we get,
$\Rightarrow {3^1} \times {5^1}$
Prime factors of \[50\]$ = 2 \times 5 \times 5$
Expressing as exponents, we get,
$\Rightarrow 2 \times {5^2}$
Now, Least common multiple is a product of common factors with highest power and all other non-common factors. We can see that five is the only common factor of \[15\] and \[50\].
Hence, least common multiple of \[15\] and \[50\]\[ = {2^1} \times {3^1} \times {5^2}\]
Evaluating the powers, we get,
\[\Rightarrow 2 \times 3 \times 25 = 150\]

Hence, the least common multiple of \[15\] and \[50\] is $5$.

Note: Least common multiple is the smallest number that is completely divisible by both the given numbers. LCM is the product of all the common factors with the highest powers and all the non-common factors. Knowledge of least common multiple is also used in addition and subtraction of fractions.