Least Common Multiple (LCM) of 142 and 199
The least common multiple (LCM) of 142 and 199 is 28258.
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 142 and 199?
First, calculate the GCD of 142 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 199 = 0 remainder 142 |
| 2 | 199 ÷ 142 = 1 remainder 57 |
| 3 | 142 ÷ 57 = 2 remainder 28 |
| 4 | 57 ÷ 28 = 2 remainder 1 |
| 5 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 120 | 7080 |
| 117 and 91 | 819 |
| 106 and 63 | 6678 |
| 88 and 112 | 1232 |
| 112 and 168 | 336 |