Least Common Multiple (LCM) of 120 and 192
The least common multiple (LCM) of 120 and 192 is 960.
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 192?
First, calculate the GCD of 120 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 192 = 0 remainder 120 |
| 2 | 192 ÷ 120 = 1 remainder 72 |
| 3 | 120 ÷ 72 = 1 remainder 48 |
| 4 | 72 ÷ 48 = 1 remainder 24 |
| 5 | 48 ÷ 24 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 43 | 2408 |
| 28 and 51 | 1428 |
| 10 and 178 | 890 |
| 183 and 113 | 20679 |
| 69 and 151 | 10419 |