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 |
|---|---|
| 100 and 128 | 3200 |
| 161 and 187 | 30107 |
| 146 and 80 | 5840 |
| 17 and 165 | 2805 |
| 25 and 116 | 2900 |