Least Common Multiple (LCM) of 125 and 196
The least common multiple (LCM) of 125 and 196 is 24500.
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 196?
First, calculate the GCD of 125 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 196 = 0 remainder 125 |
| 2 | 196 ÷ 125 = 1 remainder 71 |
| 3 | 125 ÷ 71 = 1 remainder 54 |
| 4 | 71 ÷ 54 = 1 remainder 17 |
| 5 | 54 ÷ 17 = 3 remainder 3 |
| 6 | 17 ÷ 3 = 5 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 95 | 1140 |
| 162 and 112 | 9072 |
| 102 and 140 | 7140 |
| 142 and 173 | 24566 |
| 80 and 58 | 2320 |