Least Common Multiple (LCM) of 67 and 43
The least common multiple (LCM) of 67 and 43 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 67 and 43?
First, calculate the GCD of 67 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 43 = 1 remainder 24 |
| 2 | 43 ÷ 24 = 1 remainder 19 |
| 3 | 24 ÷ 19 = 1 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 119 | 23086 |
| 197 and 15 | 2955 |
| 181 and 67 | 12127 |
| 179 and 196 | 35084 |
| 56 and 25 | 1400 |