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 |
|---|---|
| 39 and 172 | 6708 |
| 47 and 159 | 7473 |
| 171 and 34 | 5814 |
| 158 and 143 | 22594 |
| 145 and 25 | 725 |