Least Common Multiple (LCM) of 132 and 194
The least common multiple (LCM) of 132 and 194 is 12804.
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 132 and 194?
First, calculate the GCD of 132 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 194 = 0 remainder 132 |
| 2 | 194 ÷ 132 = 1 remainder 62 |
| 3 | 132 ÷ 62 = 2 remainder 8 |
| 4 | 62 ÷ 8 = 7 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 38 | 570 |
| 123 and 79 | 9717 |
| 175 and 31 | 5425 |
| 114 and 194 | 11058 |
| 27 and 129 | 1161 |