Least Common Multiple (LCM) of 199 and 157
The least common multiple (LCM) of 199 and 157 is 31243.
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 199 and 157?
First, calculate the GCD of 199 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 157 = 1 remainder 42 |
| 2 | 157 ÷ 42 = 3 remainder 31 |
| 3 | 42 ÷ 31 = 1 remainder 11 |
| 4 | 31 ÷ 11 = 2 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 24 | 1752 |
| 101 and 159 | 16059 |
| 64 and 31 | 1984 |
| 164 and 105 | 17220 |
| 37 and 79 | 2923 |