Least Common Multiple (LCM) of 188 and 55
The least common multiple (LCM) of 188 and 55 is 10340.
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 55?
First, calculate the GCD of 188 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 55 = 3 remainder 23 |
| 2 | 55 ÷ 23 = 2 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 106 | 15582 |
| 118 and 102 | 6018 |
| 188 and 47 | 188 |
| 144 and 100 | 3600 |
| 72 and 54 | 216 |