Least Common Multiple (LCM) of 118 and 135
The least common multiple (LCM) of 118 and 135 is 15930.
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 118 and 135?
First, calculate the GCD of 118 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 135 = 0 remainder 118 |
| 2 | 135 ÷ 118 = 1 remainder 17 |
| 3 | 118 ÷ 17 = 6 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 14 | 630 |
| 72 and 56 | 504 |
| 175 and 190 | 6650 |
| 147 and 85 | 12495 |
| 129 and 21 | 903 |