Least Common Multiple (LCM) of 135 and 179
The least common multiple (LCM) of 135 and 179 is 24165.
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 179?
First, calculate the GCD of 135 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 179 = 0 remainder 135 |
| 2 | 179 ÷ 135 = 1 remainder 44 |
| 3 | 135 ÷ 44 = 3 remainder 3 |
| 4 | 44 ÷ 3 = 14 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 81 | 8910 |
| 186 and 73 | 13578 |
| 46 and 186 | 4278 |
| 99 and 65 | 6435 |
| 71 and 152 | 10792 |