Least Common Multiple (LCM) of 120 and 189
The least common multiple (LCM) of 120 and 189 is 7560.
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 189?
First, calculate the GCD of 120 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 189 = 0 remainder 120 |
| 2 | 189 ÷ 120 = 1 remainder 69 |
| 3 | 120 ÷ 69 = 1 remainder 51 |
| 4 | 69 ÷ 51 = 1 remainder 18 |
| 5 | 51 ÷ 18 = 2 remainder 15 |
| 6 | 18 ÷ 15 = 1 remainder 3 |
| 7 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 75 | 3075 |
| 25 and 129 | 3225 |
| 44 and 68 | 748 |
| 69 and 103 | 7107 |
| 184 and 109 | 20056 |