Least Common Multiple (LCM) of 119 and 135
The least common multiple (LCM) of 119 and 135 is 16065.
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 119 and 135?
First, calculate the GCD of 119 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 135 = 0 remainder 119 |
| 2 | 135 ÷ 119 = 1 remainder 16 |
| 3 | 119 ÷ 16 = 7 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 180 | 16020 |
| 58 and 105 | 6090 |
| 141 and 59 | 8319 |
| 135 and 175 | 4725 |
| 179 and 86 | 15394 |