Least Common Multiple (LCM) of 59 and 109
The least common multiple (LCM) of 59 and 109 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 59 and 109?
First, calculate the GCD of 59 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 109 = 0 remainder 59 |
| 2 | 109 ÷ 59 = 1 remainder 50 |
| 3 | 59 ÷ 50 = 1 remainder 9 |
| 4 | 50 ÷ 9 = 5 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 151 | 15251 |
| 167 and 40 | 6680 |
| 43 and 147 | 6321 |
| 174 and 11 | 1914 |
| 120 and 109 | 13080 |