Least Common Multiple (LCM) of 43 and 69
The least common multiple (LCM) of 43 and 69 is 2967.
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 69?
First, calculate the GCD of 43 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 69 = 0 remainder 43 |
| 2 | 69 ÷ 43 = 1 remainder 26 |
| 3 | 43 ÷ 26 = 1 remainder 17 |
| 4 | 26 ÷ 17 = 1 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 126 | 378 |
| 114 and 67 | 7638 |
| 109 and 49 | 5341 |
| 139 and 128 | 17792 |
| 95 and 187 | 17765 |