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 |
|---|---|
| 172 and 184 | 7912 |
| 91 and 51 | 4641 |
| 11 and 153 | 1683 |
| 166 and 185 | 30710 |
| 126 and 113 | 14238 |