Least Common Multiple (LCM) of 37 and 180
The least common multiple (LCM) of 37 and 180 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 37 and 180?
First, calculate the GCD of 37 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 180 = 0 remainder 37 |
| 2 | 180 ÷ 37 = 4 remainder 32 |
| 3 | 37 ÷ 32 = 1 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 139 | 16541 |
| 138 and 47 | 6486 |
| 108 and 112 | 3024 |
| 105 and 147 | 735 |
| 34 and 165 | 5610 |