Least Common Multiple (LCM) of 188 and 75
The least common multiple (LCM) of 188 and 75 is 14100.
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 188 and 75?
First, calculate the GCD of 188 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 75 = 2 remainder 38 |
| 2 | 75 ÷ 38 = 1 remainder 37 |
| 3 | 38 ÷ 37 = 1 remainder 1 |
| 4 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 117 | 8541 |
| 101 and 180 | 18180 |
| 31 and 116 | 3596 |
| 140 and 21 | 420 |
| 85 and 21 | 1785 |