Least Common Multiple (LCM) of 50 and 188
The least common multiple (LCM) of 50 and 188 is 4700.
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 50 and 188?
First, calculate the GCD of 50 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 188 = 0 remainder 50 |
| 2 | 188 ÷ 50 = 3 remainder 38 |
| 3 | 50 ÷ 38 = 1 remainder 12 |
| 4 | 38 ÷ 12 = 3 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 189 | 7560 |
| 50 and 20 | 100 |
| 100 and 177 | 17700 |
| 164 and 52 | 2132 |
| 92 and 126 | 5796 |