Least Common Multiple (LCM) of 68 and 117
The least common multiple (LCM) of 68 and 117 is 7956.
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 117?
First, calculate the GCD of 68 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 117 = 0 remainder 68 |
| 2 | 117 ÷ 68 = 1 remainder 49 |
| 3 | 68 ÷ 49 = 1 remainder 19 |
| 4 | 49 ÷ 19 = 2 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 164 | 4756 |
| 182 and 76 | 6916 |
| 170 and 68 | 340 |
| 189 and 100 | 18900 |
| 141 and 25 | 3525 |