Least Common Multiple (LCM) of 180 and 37
The least common multiple (LCM) of 180 and 37 is 6660.
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 37?
First, calculate the GCD of 180 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 37 = 4 remainder 32 |
| 2 | 37 ÷ 32 = 1 remainder 5 |
| 3 | 32 ÷ 5 = 6 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 178 | 11214 |
| 136 and 114 | 7752 |
| 150 and 48 | 1200 |
| 190 and 45 | 1710 |
| 149 and 74 | 11026 |