Least Common Multiple (LCM) of 89 and 122
The least common multiple (LCM) of 89 and 122 is 10858.
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 122?
First, calculate the GCD of 89 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 122 = 0 remainder 89 |
| 2 | 122 ÷ 89 = 1 remainder 33 |
| 3 | 89 ÷ 33 = 2 remainder 23 |
| 4 | 33 ÷ 23 = 1 remainder 10 |
| 5 | 23 ÷ 10 = 2 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 43 | 5934 |
| 82 and 102 | 4182 |
| 53 and 152 | 8056 |
| 79 and 17 | 1343 |
| 26 and 21 | 546 |