Least Common Multiple (LCM) of 120 and 146
The least common multiple (LCM) of 120 and 146 is 8760.
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 146?
First, calculate the GCD of 120 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 146 = 0 remainder 120 |
| 2 | 146 ÷ 120 = 1 remainder 26 |
| 3 | 120 ÷ 26 = 4 remainder 16 |
| 4 | 26 ÷ 16 = 1 remainder 10 |
| 5 | 16 ÷ 10 = 1 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 172 | 1204 |
| 193 and 198 | 38214 |
| 180 and 41 | 7380 |
| 107 and 58 | 6206 |
| 156 and 199 | 31044 |