Least Common Multiple (LCM) of 199 and 61
The least common multiple (LCM) of 199 and 61 is 12139.
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 61?
First, calculate the GCD of 199 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 61 = 3 remainder 16 |
| 2 | 61 ÷ 16 = 3 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 90 | 4230 |
| 157 and 38 | 5966 |
| 174 and 108 | 3132 |
| 64 and 63 | 4032 |
| 38 and 61 | 2318 |