Least Common Multiple (LCM) of 43 and 138
The least common multiple (LCM) of 43 and 138 is 5934.
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 138?
First, calculate the GCD of 43 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 138 = 0 remainder 43 |
| 2 | 138 ÷ 43 = 3 remainder 9 |
| 3 | 43 ÷ 9 = 4 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 80 | 5360 |
| 44 and 173 | 7612 |
| 184 and 176 | 4048 |
| 48 and 127 | 6096 |
| 123 and 123 | 123 |