Least Common Multiple (LCM) of 157 and 190
The least common multiple (LCM) of 157 and 190 is 29830.
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 157 and 190?
First, calculate the GCD of 157 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 190 = 0 remainder 157 |
| 2 | 190 ÷ 157 = 1 remainder 33 |
| 3 | 157 ÷ 33 = 4 remainder 25 |
| 4 | 33 ÷ 25 = 1 remainder 8 |
| 5 | 25 ÷ 8 = 3 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 14 | 574 |
| 90 and 91 | 8190 |
| 142 and 129 | 18318 |
| 76 and 57 | 228 |
| 116 and 116 | 116 |