Least Common Multiple (LCM) of 59 and 102
The least common multiple (LCM) of 59 and 102 is 6018.
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 102?
First, calculate the GCD of 59 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 102 = 0 remainder 59 |
| 2 | 102 ÷ 59 = 1 remainder 43 |
| 3 | 59 ÷ 43 = 1 remainder 16 |
| 4 | 43 ÷ 16 = 2 remainder 11 |
| 5 | 16 ÷ 11 = 1 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 32 | 96 |
| 21 and 31 | 651 |
| 121 and 168 | 20328 |
| 95 and 99 | 9405 |
| 110 and 114 | 6270 |