Least Common Multiple (LCM) of 43 and 67
The least common multiple (LCM) of 43 and 67 is 2881.
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 67?
First, calculate the GCD of 43 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 67 = 0 remainder 43 |
| 2 | 67 ÷ 43 = 1 remainder 24 |
| 3 | 43 ÷ 24 = 1 remainder 19 |
| 4 | 24 ÷ 19 = 1 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 75 | 2850 |
| 137 and 141 | 19317 |
| 68 and 74 | 2516 |
| 187 and 51 | 561 |
| 191 and 31 | 5921 |