Least Common Multiple (LCM) of 39 and 180
The least common multiple (LCM) of 39 and 180 is 2340.
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 39 and 180?
First, calculate the GCD of 39 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 180 = 0 remainder 39 |
| 2 | 180 ÷ 39 = 4 remainder 24 |
| 3 | 39 ÷ 24 = 1 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 43 | 559 |
| 137 and 195 | 26715 |
| 19 and 164 | 3116 |
| 86 and 172 | 172 |
| 139 and 198 | 27522 |