Least Common Multiple (LCM) of 59 and 105
The least common multiple (LCM) of 59 and 105 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 59 and 105?
First, calculate the GCD of 59 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 105 = 0 remainder 59 |
| 2 | 105 ÷ 59 = 1 remainder 46 |
| 3 | 59 ÷ 46 = 1 remainder 13 |
| 4 | 46 ÷ 13 = 3 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 153 | 2295 |
| 133 and 168 | 3192 |
| 167 and 89 | 14863 |
| 125 and 123 | 15375 |
| 124 and 57 | 7068 |