Least Common Multiple (LCM) of 125 and 157
The least common multiple (LCM) of 125 and 157 is 19625.
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 157?
First, calculate the GCD of 125 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 157 = 0 remainder 125 |
| 2 | 157 ÷ 125 = 1 remainder 32 |
| 3 | 125 ÷ 32 = 3 remainder 29 |
| 4 | 32 ÷ 29 = 1 remainder 3 |
| 5 | 29 ÷ 3 = 9 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 142 | 12212 |
| 14 and 64 | 448 |
| 31 and 189 | 5859 |
| 105 and 188 | 19740 |
| 199 and 192 | 38208 |