Least Common Multiple (LCM) of 189 and 120
The least common multiple (LCM) of 189 and 120 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 189 and 120?
First, calculate the GCD of 189 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 120 = 1 remainder 69 |
| 2 | 120 ÷ 69 = 1 remainder 51 |
| 3 | 69 ÷ 51 = 1 remainder 18 |
| 4 | 51 ÷ 18 = 2 remainder 15 |
| 5 | 18 ÷ 15 = 1 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 33 | 4389 |
| 75 and 12 | 300 |
| 118 and 100 | 5900 |
| 17 and 71 | 1207 |
| 58 and 128 | 3712 |