Least Common Multiple (LCM) of 121 and 89
The least common multiple (LCM) of 121 and 89 is 10769.
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 121 and 89?
First, calculate the GCD of 121 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 89 = 1 remainder 32 |
| 2 | 89 ÷ 32 = 2 remainder 25 |
| 3 | 32 ÷ 25 = 1 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 18 | 1854 |
| 37 and 114 | 4218 |
| 89 and 149 | 13261 |
| 175 and 172 | 30100 |
| 102 and 30 | 510 |