Least Common Multiple (LCM) of 109 and 59
The least common multiple (LCM) of 109 and 59 is 6431.
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 109 and 59?
First, calculate the GCD of 109 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 59 = 1 remainder 50 |
| 2 | 59 ÷ 50 = 1 remainder 9 |
| 3 | 50 ÷ 9 = 5 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 57 | 2850 |
| 63 and 193 | 12159 |
| 150 and 28 | 2100 |
| 126 and 89 | 11214 |
| 137 and 111 | 15207 |