Least Common Multiple (LCM) of 126 and 89
The least common multiple (LCM) of 126 and 89 is 11214.
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 89?
First, calculate the GCD of 126 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 89 = 1 remainder 37 |
| 2 | 89 ÷ 37 = 2 remainder 15 |
| 3 | 37 ÷ 15 = 2 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 152 | 15656 |
| 145 and 74 | 10730 |
| 200 and 116 | 5800 |
| 146 and 148 | 10804 |
| 10 and 26 | 130 |