Least Common Multiple (LCM) of 37 and 50
The least common multiple (LCM) of 37 and 50 is 1850.
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 50?
First, calculate the GCD of 37 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 50 = 0 remainder 37 |
| 2 | 50 ÷ 37 = 1 remainder 13 |
| 3 | 37 ÷ 13 = 2 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 30 | 2940 |
| 40 and 186 | 3720 |
| 123 and 191 | 23493 |
| 139 and 188 | 26132 |
| 176 and 66 | 528 |