Least Common Multiple (LCM) of 107 and 126
The least common multiple (LCM) of 107 and 126 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 107 and 126?
First, calculate the GCD of 107 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 126 = 0 remainder 107 |
| 2 | 126 ÷ 107 = 1 remainder 19 |
| 3 | 107 ÷ 19 = 5 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 111 | 4218 |
| 171 and 36 | 684 |
| 193 and 193 | 193 |
| 107 and 17 | 1819 |
| 118 and 166 | 9794 |