Least Common Multiple (LCM) of 59 and 142
The least common multiple (LCM) of 59 and 142 is 8378.
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 142?
First, calculate the GCD of 59 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 142 = 0 remainder 59 |
| 2 | 142 ÷ 59 = 2 remainder 24 |
| 3 | 59 ÷ 24 = 2 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 70 | 350 |
| 103 and 179 | 18437 |
| 158 and 41 | 6478 |
| 182 and 107 | 19474 |
| 193 and 185 | 35705 |