Least Common Multiple (LCM) of 37 and 199
The least common multiple (LCM) of 37 and 199 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 37 and 199?
First, calculate the GCD of 37 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 199 = 0 remainder 37 |
| 2 | 199 ÷ 37 = 5 remainder 14 |
| 3 | 37 ÷ 14 = 2 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 109 | 8284 |
| 35 and 85 | 595 |
| 51 and 135 | 2295 |
| 67 and 28 | 1876 |
| 24 and 57 | 456 |