Least Common Multiple (LCM) of 102 and 59
The least common multiple (LCM) of 102 and 59 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 102 and 59?
First, calculate the GCD of 102 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 59 = 1 remainder 43 |
| 2 | 59 ÷ 43 = 1 remainder 16 |
| 3 | 43 ÷ 16 = 2 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 |
|---|---|
| 165 and 81 | 4455 |
| 43 and 148 | 6364 |
| 39 and 31 | 1209 |
| 179 and 145 | 25955 |
| 181 and 157 | 28417 |