Least Common Multiple (LCM) of 55 and 194
The least common multiple (LCM) of 55 and 194 is 10670.
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 194?
First, calculate the GCD of 55 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 194 = 0 remainder 55 |
| 2 | 194 ÷ 55 = 3 remainder 29 |
| 3 | 55 ÷ 29 = 1 remainder 26 |
| 4 | 29 ÷ 26 = 1 remainder 3 |
| 5 | 26 ÷ 3 = 8 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 66 | 8778 |
| 10 and 132 | 660 |
| 60 and 146 | 4380 |
| 88 and 49 | 4312 |
| 110 and 99 | 990 |