Least Common Multiple (LCM) of 43 and 60
The least common multiple (LCM) of 43 and 60 is 2580.
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 60?
First, calculate the GCD of 43 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 60 = 0 remainder 43 |
| 2 | 60 ÷ 43 = 1 remainder 17 |
| 3 | 43 ÷ 17 = 2 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 108 | 2700 |
| 140 and 49 | 980 |
| 178 and 57 | 10146 |
| 157 and 86 | 13502 |
| 105 and 68 | 7140 |