Least Common Multiple (LCM) of 180 and 114
The least common multiple (LCM) of 180 and 114 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 180 and 114?
First, calculate the GCD of 180 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 114 = 1 remainder 66 |
| 2 | 114 ÷ 66 = 1 remainder 48 |
| 3 | 66 ÷ 48 = 1 remainder 18 |
| 4 | 48 ÷ 18 = 2 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 65 | 65 |
| 30 and 185 | 1110 |
| 85 and 173 | 14705 |
| 51 and 11 | 561 |
| 23 and 92 | 92 |