Least Common Multiple (LCM) of 135 and 114
The least common multiple (LCM) of 135 and 114 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 135 and 114?
First, calculate the GCD of 135 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 114 = 1 remainder 21 |
| 2 | 114 ÷ 21 = 5 remainder 9 |
| 3 | 21 ÷ 9 = 2 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 60 | 1140 |
| 62 and 152 | 4712 |
| 135 and 13 | 1755 |
| 22 and 77 | 154 |
| 124 and 83 | 10292 |