Least Common Multiple (LCM) of 59 and 121
The least common multiple (LCM) of 59 and 121 is 7139.
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 121?
First, calculate the GCD of 59 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 121 = 0 remainder 59 |
| 2 | 121 ÷ 59 = 2 remainder 3 |
| 3 | 59 ÷ 3 = 19 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 80 | 3280 |
| 172 and 169 | 29068 |
| 193 and 133 | 25669 |
| 175 and 173 | 30275 |
| 139 and 149 | 20711 |