Least Common Multiple (LCM) of 43 and 84
The least common multiple (LCM) of 43 and 84 is 3612.
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 84?
First, calculate the GCD of 43 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 84 = 0 remainder 43 |
| 2 | 84 ÷ 43 = 1 remainder 41 |
| 3 | 43 ÷ 41 = 1 remainder 2 |
| 4 | 41 ÷ 2 = 20 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 15 | 300 |
| 174 and 59 | 10266 |
| 128 and 107 | 13696 |
| 131 and 124 | 16244 |
| 69 and 128 | 8832 |