Least Common Multiple (LCM) of 113 and 68
The least common multiple (LCM) of 113 and 68 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 113 and 68?
First, calculate the GCD of 113 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 68 = 1 remainder 45 |
| 2 | 68 ÷ 45 = 1 remainder 23 |
| 3 | 45 ÷ 23 = 1 remainder 22 |
| 4 | 23 ÷ 22 = 1 remainder 1 |
| 5 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 57 | 4560 |
| 175 and 132 | 23100 |
| 67 and 172 | 11524 |
| 47 and 76 | 3572 |
| 142 and 53 | 7526 |