Question

How do you find the least common multiple of 10 and 3?

Answer 1

Hint: The above question is an example for LCM i.e., least common multiple where we have to calculate the least common multiple from the multiples of 10 and from the multiples of 3 or we can even find using a formula. The common smallest number found in both the multiples of numbers will be the LCM

Complete step by step answer:
LCM means the lowest or least common multiples. The result of LCM should be the smallest positive number that divides both the numbers without any remainder.
If a and b are two integers then the formula for calculating lcm is as follows:
\[lcm(a,b) = \dfrac{{|a \times b|}}{{\gcd (a,b)}}\]
where \[lcm(a,b)\] is the least common multiple of integers
\[\gcd (a,b)\] is the greatest common divisor of integers a and b
GCD is the largest positive integer that divides both the numbers without any remainder
The above-given numbers are 10 and 3.So, we first need to prime factorize the numbers 10 and 3.
For 10 the divisor can be,
1,2,5
For 3 the divisor can be,
\[1\]
So, the common divisor is 1.
Therefore, by substituting it in the formula we get, \[\]
 $
  lcm(a,b) = \dfrac{{|10 \times 3|}}{1} \\
  lcm(a,b) = 30 \\
  $
Therefore, the least common multiple of 3 and 10 is 30.

Note:
An alternative method to calculate LCM of 10 and 3 is by checking the common multiples. For the number 10 multiples are 10,20,30,40 and so on and for the number 3 is 3,6,9…30. So here the common multiples which are least or lowest are 30.