Least Common Multiple (LCM) of 108 and 43
The least common multiple (LCM) of 108 and 43 is 4644.
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 108 and 43?
First, calculate the GCD of 108 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 43 = 2 remainder 22 |
| 2 | 43 ÷ 22 = 1 remainder 21 |
| 3 | 22 ÷ 21 = 1 remainder 1 |
| 4 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 187 | 6919 |
| 13 and 103 | 1339 |
| 73 and 90 | 6570 |
| 186 and 31 | 186 |
| 164 and 152 | 6232 |