Least Common Multiple (LCM) of 158 and 199
The least common multiple (LCM) of 158 and 199 is 31442.
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 158 and 199?
First, calculate the GCD of 158 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 158 ÷ 199 = 0 remainder 158 |
| 2 | 199 ÷ 158 = 1 remainder 41 |
| 3 | 158 ÷ 41 = 3 remainder 35 |
| 4 | 41 ÷ 35 = 1 remainder 6 |
| 5 | 35 ÷ 6 = 5 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 116 | 4060 |
| 75 and 51 | 1275 |
| 43 and 96 | 4128 |
| 194 and 54 | 5238 |
| 97 and 124 | 12028 |