Least Common Multiple (LCM) of 117 and 68
The least common multiple (LCM) of 117 and 68 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 117 and 68?
First, calculate the GCD of 117 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 68 = 1 remainder 49 |
| 2 | 68 ÷ 49 = 1 remainder 19 |
| 3 | 49 ÷ 19 = 2 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 19 | 2489 |
| 199 and 84 | 16716 |
| 42 and 155 | 6510 |
| 107 and 121 | 12947 |
| 165 and 195 | 2145 |