Least Common Multiple (LCM) of 156 and 180
The least common multiple (LCM) of 156 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 156 and 180?
First, calculate the GCD of 156 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 180 = 0 remainder 156 |
| 2 | 180 ÷ 156 = 1 remainder 24 |
| 3 | 156 ÷ 24 = 6 remainder 12 |
| 4 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 27 | 4995 |
| 45 and 54 | 270 |
| 45 and 144 | 720 |
| 193 and 57 | 11001 |
| 55 and 164 | 9020 |