Least Common Multiple (LCM) of 134 and 111
The least common multiple (LCM) of 134 and 111 is 14874.
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 111?
First, calculate the GCD of 134 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 111 = 1 remainder 23 |
| 2 | 111 ÷ 23 = 4 remainder 19 |
| 3 | 23 ÷ 19 = 1 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 163 | 163 |
| 129 and 156 | 6708 |
| 30 and 50 | 150 |
| 21 and 34 | 714 |
| 116 and 12 | 348 |