Least Common Multiple (LCM) of 188 and 105
The least common multiple (LCM) of 188 and 105 is 19740.
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 105?
First, calculate the GCD of 188 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 105 = 1 remainder 83 |
| 2 | 105 ÷ 83 = 1 remainder 22 |
| 3 | 83 ÷ 22 = 3 remainder 17 |
| 4 | 22 ÷ 17 = 1 remainder 5 |
| 5 | 17 ÷ 5 = 3 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 154 | 10472 |
| 198 and 48 | 1584 |
| 87 and 90 | 2610 |
| 188 and 112 | 5264 |
| 97 and 54 | 5238 |