Least Common Multiple (LCM) of 114 and 180
The least common multiple (LCM) of 114 and 180 is 3420.
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 114 and 180?
First, calculate the GCD of 114 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 180 = 0 remainder 114 |
| 2 | 180 ÷ 114 = 1 remainder 66 |
| 3 | 114 ÷ 66 = 1 remainder 48 |
| 4 | 66 ÷ 48 = 1 remainder 18 |
| 5 | 48 ÷ 18 = 2 remainder 12 |
| 6 | 18 ÷ 12 = 1 remainder 6 |
| 7 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 96 | 6240 |
| 175 and 162 | 28350 |
| 141 and 84 | 3948 |
| 70 and 173 | 12110 |
| 170 and 200 | 3400 |