Least Common Multiple (LCM) of 43 and 52
The least common multiple (LCM) of 43 and 52 is 2236.
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 52?
First, calculate the GCD of 43 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 52 = 0 remainder 43 |
| 2 | 52 ÷ 43 = 1 remainder 9 |
| 3 | 43 ÷ 9 = 4 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 130 | 2470 |
| 70 and 188 | 6580 |
| 130 and 127 | 16510 |
| 107 and 142 | 15194 |
| 135 and 98 | 13230 |