Least Common Multiple (LCM) of 59 and 75
The least common multiple (LCM) of 59 and 75 is 4425.
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 75?
First, calculate the GCD of 59 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 75 = 0 remainder 59 |
| 2 | 75 ÷ 59 = 1 remainder 16 |
| 3 | 59 ÷ 16 = 3 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 107 | 7918 |
| 45 and 198 | 990 |
| 99 and 192 | 6336 |
| 23 and 82 | 1886 |
| 194 and 117 | 22698 |