Least Common Multiple (LCM) of 199 and 37
The least common multiple (LCM) of 199 and 37 is 7363.
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 37?
First, calculate the GCD of 199 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 37 = 5 remainder 14 |
| 2 | 37 ÷ 14 = 2 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 89 | 12371 |
| 47 and 121 | 5687 |
| 98 and 29 | 2842 |
| 143 and 87 | 12441 |
| 68 and 57 | 3876 |