Least Common Multiple (LCM) of 126 and 107
The least common multiple (LCM) of 126 and 107 is 13482.
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 107?
First, calculate the GCD of 126 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 107 = 1 remainder 19 |
| 2 | 107 ÷ 19 = 5 remainder 12 |
| 3 | 19 ÷ 12 = 1 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 38 | 1862 |
| 139 and 177 | 24603 |
| 79 and 144 | 11376 |
| 90 and 25 | 450 |
| 30 and 159 | 1590 |