Least Common Multiple (LCM) of 107 and 43
The least common multiple (LCM) of 107 and 43 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 107 and 43?
First, calculate the GCD of 107 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 43 = 2 remainder 21 |
| 2 | 43 ÷ 21 = 2 remainder 1 |
| 3 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 78 | 936 |
| 101 and 88 | 8888 |
| 105 and 55 | 1155 |
| 147 and 191 | 28077 |
| 151 and 144 | 21744 |