Least Common Multiple (LCM) of 68 and 54
The least common multiple (LCM) of 68 and 54 is 1836.
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 54?
First, calculate the GCD of 68 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 54 = 1 remainder 14 |
| 2 | 54 ÷ 14 = 3 remainder 12 |
| 3 | 14 ÷ 12 = 1 remainder 2 |
| 4 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 85 | 170 |
| 83 and 62 | 5146 |
| 106 and 133 | 14098 |
| 138 and 30 | 690 |
| 164 and 85 | 13940 |