Least Common Multiple (LCM) of 18 and 43
The least common multiple (LCM) of 18 and 43 is 774.
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 18 and 43?
First, calculate the GCD of 18 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 43 = 0 remainder 18 |
| 2 | 43 ÷ 18 = 2 remainder 7 |
| 3 | 18 ÷ 7 = 2 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 13 | 1339 |
| 88 and 156 | 3432 |
| 113 and 75 | 8475 |
| 79 and 96 | 7584 |
| 146 and 91 | 13286 |