Least Common Multiple (LCM) of 138 and 180
The least common multiple (LCM) of 138 and 180 is 4140.
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 138 and 180?
First, calculate the GCD of 138 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 180 = 0 remainder 138 |
| 2 | 180 ÷ 138 = 1 remainder 42 |
| 3 | 138 ÷ 42 = 3 remainder 12 |
| 4 | 42 ÷ 12 = 3 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 86 | 7052 |
| 22 and 34 | 374 |
| 165 and 72 | 3960 |
| 53 and 78 | 4134 |
| 172 and 57 | 9804 |