Least Common Multiple (LCM) of 75 and 188
The least common multiple (LCM) of 75 and 188 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 75 and 188?
First, calculate the GCD of 75 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 188 = 0 remainder 75 |
| 2 | 188 ÷ 75 = 2 remainder 38 |
| 3 | 75 ÷ 38 = 1 remainder 37 |
| 4 | 38 ÷ 37 = 1 remainder 1 |
| 5 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 160 | 3360 |
| 95 and 200 | 3800 |
| 169 and 30 | 5070 |
| 153 and 196 | 29988 |
| 112 and 101 | 11312 |