Least Common Multiple (LCM) of 135 and 117
The least common multiple (LCM) of 135 and 117 is 1755.
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 117?
First, calculate the GCD of 135 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 117 = 1 remainder 18 |
| 2 | 117 ÷ 18 = 6 remainder 9 |
| 3 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 168 | 4200 |
| 10 and 119 | 1190 |
| 12 and 11 | 132 |
| 85 and 141 | 11985 |
| 154 and 86 | 6622 |