The least common multiple, or LCM, of two numbers is the smallest value divisible by both the numbers, or it’s the smallest number that both your numbers divide into evenly.
The LCM can be found by finding the GCF, or greatest common factors, and the remaining factors.
Next Lesson: Greatest Common Factor
The transcript is for your convenience
The LCM is the product of the GCF and those remaining factors. The LCM is the product of the GCF and those remaining factors.
For example, if we wanted to find the LCM of 18 and 30, we would first need to factor them. 18 is 2*9. Since 9 is not prime, we would factor to 3*3.
30 is also even, so we’ll start with 2. 30 is 2*15, 15 is not prime, so we factor 15. 15 is 3*5.
The GCF, or greatest common factor, is 2*3, or 6.
So, our least common multiple is the product of our GCF, 6, and the remaining factors.
The remaining factors are 3 and 5, so 6*3*5. 6*5 is 30, 30*3 is 90. So, the smallest number that 18 and 30 will both divide into evenly is 90.
A more systematic way to find the LCM of some given integers is to use prime factorization.
Prime factorization involves breaking down each of the numbers being compared into its product of prime numbers. The LCM is then determined by multiplying the highest power of each prime number together.