Least Common Multiple (LCM) of 61 and 199
The least common multiple (LCM) of 61 and 199 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 61 and 199?
First, calculate the GCD of 61 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 199 = 0 remainder 61 |
| 2 | 199 ÷ 61 = 3 remainder 16 |
| 3 | 61 ÷ 16 = 3 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 34 | 3570 |
| 171 and 47 | 8037 |
| 16 and 25 | 400 |
| 162 and 20 | 1620 |
| 113 and 78 | 8814 |