Least Common Multiple (LCM) of 120 and 183
The least common multiple (LCM) of 120 and 183 is 7320.
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 183?
First, calculate the GCD of 120 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 183 = 0 remainder 120 |
| 2 | 183 ÷ 120 = 1 remainder 63 |
| 3 | 120 ÷ 63 = 1 remainder 57 |
| 4 | 63 ÷ 57 = 1 remainder 6 |
| 5 | 57 ÷ 6 = 9 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 33 | 3597 |
| 163 and 187 | 30481 |
| 148 and 81 | 11988 |
| 23 and 24 | 552 |
| 192 and 188 | 9024 |