Least Common Multiple (LCM) of 125 and 199
The least common multiple (LCM) of 125 and 199 is 24875.
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 199?
First, calculate the GCD of 125 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 199 = 0 remainder 125 |
| 2 | 199 ÷ 125 = 1 remainder 74 |
| 3 | 125 ÷ 74 = 1 remainder 51 |
| 4 | 74 ÷ 51 = 1 remainder 23 |
| 5 | 51 ÷ 23 = 2 remainder 5 |
| 6 | 23 ÷ 5 = 4 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 66 | 2970 |
| 103 and 136 | 14008 |
| 181 and 87 | 15747 |
| 48 and 197 | 9456 |
| 152 and 148 | 5624 |