Least Common Multiple (LCM) of 134 and 189
The least common multiple (LCM) of 134 and 189 is 25326.
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 189?
First, calculate the GCD of 134 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 189 = 0 remainder 134 |
| 2 | 189 ÷ 134 = 1 remainder 55 |
| 3 | 134 ÷ 55 = 2 remainder 24 |
| 4 | 55 ÷ 24 = 2 remainder 7 |
| 5 | 24 ÷ 7 = 3 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 24 | 3576 |
| 53 and 56 | 2968 |
| 35 and 73 | 2555 |
| 21 and 195 | 1365 |
| 103 and 68 | 7004 |