Least Common Multiple (LCM) of 115 and 126
The least common multiple (LCM) of 115 and 126 is 14490.
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 115 and 126?
First, calculate the GCD of 115 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 126 = 0 remainder 115 |
| 2 | 126 ÷ 115 = 1 remainder 11 |
| 3 | 115 ÷ 11 = 10 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 105 | 3045 |
| 103 and 162 | 16686 |
| 100 and 161 | 16100 |
| 45 and 148 | 6660 |
| 11 and 70 | 770 |