Least Common Multiple (LCM) of 135 and 59
The least common multiple (LCM) of 135 and 59 is 7965.
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 135 and 59?
First, calculate the GCD of 135 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 59 = 2 remainder 17 |
| 2 | 59 ÷ 17 = 3 remainder 8 |
| 3 | 17 ÷ 8 = 2 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 45 | 8145 |
| 200 and 98 | 9800 |
| 126 and 154 | 1386 |
| 48 and 116 | 1392 |
| 68 and 60 | 1020 |