Least Common Multiple (LCM) of 105 and 59
The least common multiple (LCM) of 105 and 59 is 6195.
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 105 and 59?
First, calculate the GCD of 105 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 59 = 1 remainder 46 |
| 2 | 59 ÷ 46 = 1 remainder 13 |
| 3 | 46 ÷ 13 = 3 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 180 | 13140 |
| 63 and 20 | 1260 |
| 70 and 199 | 13930 |
| 156 and 101 | 15756 |
| 45 and 49 | 2205 |