Least Common Multiple (LCM) of 180 and 134
The least common multiple (LCM) of 180 and 134 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 180 and 134?
First, calculate the GCD of 180 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 134 = 1 remainder 46 |
| 2 | 134 ÷ 46 = 2 remainder 42 |
| 3 | 46 ÷ 42 = 1 remainder 4 |
| 4 | 42 ÷ 4 = 10 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 133 | 18354 |
| 100 and 169 | 16900 |
| 96 and 133 | 12768 |
| 143 and 152 | 21736 |
| 144 and 30 | 720 |