Least Common Multiple (LCM) of 89 and 126
The least common multiple (LCM) of 89 and 126 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 89 and 126?
First, calculate the GCD of 89 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 126 = 0 remainder 89 |
| 2 | 126 ÷ 89 = 1 remainder 37 |
| 3 | 89 ÷ 37 = 2 remainder 15 |
| 4 | 37 ÷ 15 = 2 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 70 | 1400 |
| 196 and 19 | 3724 |
| 131 and 170 | 22270 |
| 41 and 76 | 3116 |
| 172 and 96 | 4128 |