Least Common Multiple (LCM) of 189 and 157
The least common multiple (LCM) of 189 and 157 is 29673.
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 189 and 157?
First, calculate the GCD of 189 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 157 = 1 remainder 32 |
| 2 | 157 ÷ 32 = 4 remainder 29 |
| 3 | 32 ÷ 29 = 1 remainder 3 |
| 4 | 29 ÷ 3 = 9 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 108 | 7020 |
| 127 and 42 | 5334 |
| 57 and 91 | 5187 |
| 170 and 108 | 9180 |
| 116 and 185 | 21460 |