Least Common Multiple (LCM) of 126 and 199
The least common multiple (LCM) of 126 and 199 is 25074.
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 126 and 199?
First, calculate the GCD of 126 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 199 = 0 remainder 126 |
| 2 | 199 ÷ 126 = 1 remainder 73 |
| 3 | 126 ÷ 73 = 1 remainder 53 |
| 4 | 73 ÷ 53 = 1 remainder 20 |
| 5 | 53 ÷ 20 = 2 remainder 13 |
| 6 | 20 ÷ 13 = 1 remainder 7 |
| 7 | 13 ÷ 7 = 1 remainder 6 |
| 8 | 7 ÷ 6 = 1 remainder 1 |
| 9 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 124 | 7316 |
| 32 and 133 | 4256 |
| 46 and 61 | 2806 |
| 108 and 133 | 14364 |
| 85 and 74 | 6290 |