Least Common Multiple (LCM) of 180 and 68
The least common multiple (LCM) of 180 and 68 is 3060.
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 68?
First, calculate the GCD of 180 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 68 = 2 remainder 44 |
| 2 | 68 ÷ 44 = 1 remainder 24 |
| 3 | 44 ÷ 24 = 1 remainder 20 |
| 4 | 24 ÷ 20 = 1 remainder 4 |
| 5 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 15 | 2220 |
| 81 and 184 | 14904 |
| 78 and 92 | 3588 |
| 21 and 159 | 1113 |
| 184 and 45 | 8280 |