Least Common Multiple (LCM) of 180 and 50
The least common multiple (LCM) of 180 and 50 is 900.
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 50?
First, calculate the GCD of 180 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 50 = 3 remainder 30 |
| 2 | 50 ÷ 30 = 1 remainder 20 |
| 3 | 30 ÷ 20 = 1 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 116 | 15428 |
| 184 and 64 | 1472 |
| 160 and 31 | 4960 |
| 189 and 187 | 35343 |
| 64 and 74 | 2368 |