Least Common Multiple (LCM) of 134 and 180
The least common multiple (LCM) of 134 and 180 is 12060.
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 134 and 180?
First, calculate the GCD of 134 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 180 = 0 remainder 134 |
| 2 | 180 ÷ 134 = 1 remainder 46 |
| 3 | 134 ÷ 46 = 2 remainder 42 |
| 4 | 46 ÷ 42 = 1 remainder 4 |
| 5 | 42 ÷ 4 = 10 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 183 | 6771 |
| 123 and 197 | 24231 |
| 170 and 72 | 6120 |
| 74 and 99 | 7326 |
| 160 and 63 | 10080 |