Least Common Multiple (LCM) of 55 and 188
The least common multiple (LCM) of 55 and 188 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 55 and 188?
First, calculate the GCD of 55 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 188 = 0 remainder 55 |
| 2 | 188 ÷ 55 = 3 remainder 23 |
| 3 | 55 ÷ 23 = 2 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 117 | 5148 |
| 133 and 167 | 22211 |
| 53 and 198 | 10494 |
| 91 and 178 | 16198 |
| 108 and 185 | 19980 |