Least Common Multiple (LCM) of 139 and 180
The least common multiple (LCM) of 139 and 180 is 25020.
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 139 and 180?
First, calculate the GCD of 139 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 180 = 0 remainder 139 |
| 2 | 180 ÷ 139 = 1 remainder 41 |
| 3 | 139 ÷ 41 = 3 remainder 16 |
| 4 | 41 ÷ 16 = 2 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 78 | 2262 |
| 120 and 123 | 4920 |
| 134 and 137 | 18358 |
| 106 and 107 | 11342 |
| 75 and 144 | 3600 |