Least Common Multiple (LCM) of 43 and 134
The least common multiple (LCM) of 43 and 134 is 5762.
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 43 and 134?
First, calculate the GCD of 43 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 134 = 0 remainder 43 |
| 2 | 134 ÷ 43 = 3 remainder 5 |
| 3 | 43 ÷ 5 = 8 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 168 | 168 |
| 186 and 180 | 5580 |
| 45 and 124 | 5580 |
| 180 and 83 | 14940 |
| 131 and 111 | 14541 |