Least Common Multiple (LCM) of 199 and 126
The least common multiple (LCM) of 199 and 126 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 199 and 126?
First, calculate the GCD of 199 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 126 = 1 remainder 73 |
| 2 | 126 ÷ 73 = 1 remainder 53 |
| 3 | 73 ÷ 53 = 1 remainder 20 |
| 4 | 53 ÷ 20 = 2 remainder 13 |
| 5 | 20 ÷ 13 = 1 remainder 7 |
| 6 | 13 ÷ 7 = 1 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 38 | 874 |
| 100 and 100 | 100 |
| 108 and 140 | 3780 |
| 127 and 132 | 16764 |
| 178 and 39 | 6942 |