Least Common Multiple (LCM) of 68 and 107
The least common multiple (LCM) of 68 and 107 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 68 and 107?
First, calculate the GCD of 68 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 107 = 0 remainder 68 |
| 2 | 107 ÷ 68 = 1 remainder 39 |
| 3 | 68 ÷ 39 = 1 remainder 29 |
| 4 | 39 ÷ 29 = 1 remainder 10 |
| 5 | 29 ÷ 10 = 2 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 85 | 4760 |
| 124 and 153 | 18972 |
| 186 and 46 | 4278 |
| 26 and 96 | 1248 |
| 145 and 180 | 5220 |