Least Common Multiple (LCM) of 120 and 89
The least common multiple (LCM) of 120 and 89 is 10680.
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 120 and 89?
First, calculate the GCD of 120 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 89 = 1 remainder 31 |
| 2 | 89 ÷ 31 = 2 remainder 27 |
| 3 | 31 ÷ 27 = 1 remainder 4 |
| 4 | 27 ÷ 4 = 6 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 86 | 7654 |
| 76 and 187 | 14212 |
| 184 and 149 | 27416 |
| 27 and 91 | 2457 |
| 156 and 103 | 16068 |