Least Common Multiple (LCM) of 114 and 135
The least common multiple (LCM) of 114 and 135 is 5130.
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 114 and 135?
First, calculate the GCD of 114 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 135 = 0 remainder 114 |
| 2 | 135 ÷ 114 = 1 remainder 21 |
| 3 | 114 ÷ 21 = 5 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 38 | 760 |
| 38 and 147 | 5586 |
| 77 and 143 | 1001 |
| 19 and 87 | 1653 |
| 13 and 105 | 1365 |