Least Common Multiple (LCM) of 186 and 157
The least common multiple (LCM) of 186 and 157 is 29202.
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 186 and 157?
First, calculate the GCD of 186 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 157 = 1 remainder 29 |
| 2 | 157 ÷ 29 = 5 remainder 12 |
| 3 | 29 ÷ 12 = 2 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 90 | 2520 |
| 65 and 115 | 1495 |
| 188 and 108 | 5076 |
| 164 and 89 | 14596 |
| 173 and 199 | 34427 |