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 |
|---|---|
| 132 and 182 | 12012 |
| 106 and 182 | 9646 |
| 191 and 160 | 30560 |
| 118 and 24 | 1416 |
| 99 and 139 | 13761 |