Least Common Multiple (LCM) of 43 and 107
The least common multiple (LCM) of 43 and 107 is 4601.
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 107?
First, calculate the GCD of 43 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 107 = 0 remainder 43 |
| 2 | 107 ÷ 43 = 2 remainder 21 |
| 3 | 43 ÷ 21 = 2 remainder 1 |
| 4 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 128 | 16512 |
| 58 and 114 | 3306 |
| 188 and 74 | 6956 |
| 188 and 129 | 24252 |
| 114 and 151 | 17214 |