Least Common Multiple (LCM) of 180 and 139
The least common multiple (LCM) of 180 and 139 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 180 and 139?
First, calculate the GCD of 180 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 139 = 1 remainder 41 |
| 2 | 139 ÷ 41 = 3 remainder 16 |
| 3 | 41 ÷ 16 = 2 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 14 | 462 |
| 120 and 116 | 3480 |
| 73 and 17 | 1241 |
| 128 and 89 | 11392 |
| 33 and 58 | 1914 |