Least Common Multiple (LCM) of 199 and 125
The least common multiple (LCM) of 199 and 125 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 199 and 125?
First, calculate the GCD of 199 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 125 = 1 remainder 74 |
| 2 | 125 ÷ 74 = 1 remainder 51 |
| 3 | 74 ÷ 51 = 1 remainder 23 |
| 4 | 51 ÷ 23 = 2 remainder 5 |
| 5 | 23 ÷ 5 = 4 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 98 | 9114 |
| 181 and 21 | 3801 |
| 30 and 112 | 1680 |
| 120 and 171 | 6840 |
| 155 and 137 | 21235 |