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 |
|---|---|
| 174 and 53 | 9222 |
| 123 and 29 | 3567 |
| 134 and 10 | 670 |
| 115 and 56 | 6440 |
| 22 and 56 | 616 |