Least Common Multiple (LCM) of 125 and 19
The least common multiple (LCM) of 125 and 19 is 2375.
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 125 and 19?
First, calculate the GCD of 125 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 19 = 6 remainder 11 |
| 2 | 19 ÷ 11 = 1 remainder 8 |
| 3 | 11 ÷ 8 = 1 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 93 | 1302 |
| 102 and 138 | 2346 |
| 128 and 151 | 19328 |
| 125 and 175 | 875 |
| 36 and 168 | 504 |