Least Common Multiple (LCM) of 59 and 43
The least common multiple (LCM) of 59 and 43 is 2537.
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 59 and 43?
First, calculate the GCD of 59 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 43 = 1 remainder 16 |
| 2 | 43 ÷ 16 = 2 remainder 11 |
| 3 | 16 ÷ 11 = 1 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 152 | 152 |
| 80 and 200 | 400 |
| 100 and 123 | 12300 |
| 98 and 58 | 2842 |
| 109 and 44 | 4796 |