Least Common Multiple (LCM) of 68 and 135
The least common multiple (LCM) of 68 and 135 is 9180.
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 68 and 135?
First, calculate the GCD of 68 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 135 = 0 remainder 68 |
| 2 | 135 ÷ 68 = 1 remainder 67 |
| 3 | 68 ÷ 67 = 1 remainder 1 |
| 4 | 67 ÷ 1 = 67 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 60 | 1140 |
| 67 and 82 | 5494 |
| 196 and 39 | 7644 |
| 27 and 41 | 1107 |
| 174 and 144 | 4176 |