Least Common Multiple (LCM) of 55 and 68
The least common multiple (LCM) of 55 and 68 is 3740.
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 55 and 68?
First, calculate the GCD of 55 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 68 = 0 remainder 55 |
| 2 | 68 ÷ 55 = 1 remainder 13 |
| 3 | 55 ÷ 13 = 4 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 198 | 7920 |
| 54 and 14 | 378 |
| 153 and 103 | 15759 |
| 108 and 188 | 5076 |
| 148 and 37 | 148 |