Least Common Multiple (LCM) of 108 and 19
The least common multiple (LCM) of 108 and 19 is 2052.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 108 and 19?
First, calculate the GCD of 108 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 19 = 5 remainder 13 |
| 2 | 19 ÷ 13 = 1 remainder 6 |
| 3 | 13 ÷ 6 = 2 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 173 | 3806 |
| 28 and 127 | 3556 |
| 39 and 91 | 273 |
| 153 and 54 | 918 |
| 135 and 124 | 16740 |