Least Common Multiple (LCM) of 68 and 113
The least common multiple (LCM) of 68 and 113 is 7684.
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 113?
First, calculate the GCD of 68 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 113 = 0 remainder 68 |
| 2 | 113 ÷ 68 = 1 remainder 45 |
| 3 | 68 ÷ 45 = 1 remainder 23 |
| 4 | 45 ÷ 23 = 1 remainder 22 |
| 5 | 23 ÷ 22 = 1 remainder 1 |
| 6 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 66 | 1122 |
| 132 and 127 | 16764 |
| 105 and 126 | 630 |
| 170 and 88 | 7480 |
| 43 and 29 | 1247 |