Least Common Multiple (LCM) of 30 and 180
The least common multiple (LCM) of 30 and 180 is 180.
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 30 and 180?
First, calculate the GCD of 30 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 180 = 0 remainder 30 |
| 2 | 180 ÷ 30 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 33 | 660 |
| 134 and 22 | 1474 |
| 124 and 149 | 18476 |
| 82 and 170 | 6970 |
| 199 and 169 | 33631 |