Least Common Multiple (LCM) of 59 and 80
The least common multiple (LCM) of 59 and 80 is 4720.
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 80?
First, calculate the GCD of 59 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 80 = 0 remainder 59 |
| 2 | 80 ÷ 59 = 1 remainder 21 |
| 3 | 59 ÷ 21 = 2 remainder 17 |
| 4 | 21 ÷ 17 = 1 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 131 | 5502 |
| 50 and 10 | 50 |
| 184 and 115 | 920 |
| 37 and 54 | 1998 |
| 31 and 187 | 5797 |