Least Common Multiple (LCM) of 89 and 121
The least common multiple (LCM) of 89 and 121 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 89 and 121?
First, calculate the GCD of 89 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 121 = 0 remainder 89 |
| 2 | 121 ÷ 89 = 1 remainder 32 |
| 3 | 89 ÷ 32 = 2 remainder 25 |
| 4 | 32 ÷ 25 = 1 remainder 7 |
| 5 | 25 ÷ 7 = 3 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 179 | 25776 |
| 46 and 26 | 598 |
| 62 and 122 | 3782 |
| 40 and 39 | 1560 |
| 43 and 111 | 4773 |