Least Common Multiple (LCM) of 135 and 168
The least common multiple (LCM) of 135 and 168 is 7560.
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 168?
First, calculate the GCD of 135 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 168 = 0 remainder 135 |
| 2 | 168 ÷ 135 = 1 remainder 33 |
| 3 | 135 ÷ 33 = 4 remainder 3 |
| 4 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 13 | 312 |
| 193 and 38 | 7334 |
| 157 and 159 | 24963 |
| 125 and 138 | 17250 |
| 191 and 27 | 5157 |