Least Common Multiple (LCM) of 157 and 199
The least common multiple (LCM) of 157 and 199 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 157 and 199?
First, calculate the GCD of 157 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 199 = 0 remainder 157 |
| 2 | 199 ÷ 157 = 1 remainder 42 |
| 3 | 157 ÷ 42 = 3 remainder 31 |
| 4 | 42 ÷ 31 = 1 remainder 11 |
| 5 | 31 ÷ 11 = 2 remainder 9 |
| 6 | 11 ÷ 9 = 1 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 103 | 12669 |
| 171 and 88 | 15048 |
| 196 and 120 | 5880 |
| 111 and 92 | 10212 |
| 119 and 196 | 3332 |