Least Common Multiple (LCM) of 199 and 60
The least common multiple (LCM) of 199 and 60 is 11940.
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 60?
First, calculate the GCD of 199 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 60 = 3 remainder 19 |
| 2 | 60 ÷ 19 = 3 remainder 3 |
| 3 | 19 ÷ 3 = 6 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 126 | 1260 |
| 157 and 53 | 8321 |
| 121 and 65 | 7865 |
| 135 and 41 | 5535 |
| 119 and 126 | 2142 |