Least Common Multiple (LCM) of 107 and 68
The least common multiple (LCM) of 107 and 68 is 7276.
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 107 and 68?
First, calculate the GCD of 107 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 68 = 1 remainder 39 |
| 2 | 68 ÷ 39 = 1 remainder 29 |
| 3 | 39 ÷ 29 = 1 remainder 10 |
| 4 | 29 ÷ 10 = 2 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 177 | 5487 |
| 40 and 20 | 40 |
| 89 and 175 | 15575 |
| 140 and 46 | 3220 |
| 56 and 120 | 840 |