Least Common Multiple (LCM) of 180 and 39
The least common multiple (LCM) of 180 and 39 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 180 and 39?
First, calculate the GCD of 180 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 39 = 4 remainder 24 |
| 2 | 39 ÷ 24 = 1 remainder 15 |
| 3 | 24 ÷ 15 = 1 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 84 | 2772 |
| 109 and 93 | 10137 |
| 71 and 119 | 8449 |
| 101 and 49 | 4949 |
| 140 and 135 | 3780 |