Least Common Multiple (LCM) of 113 and 69
The least common multiple (LCM) of 113 and 69 is 7797.
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 69?
First, calculate the GCD of 113 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 69 = 1 remainder 44 |
| 2 | 69 ÷ 44 = 1 remainder 25 |
| 3 | 44 ÷ 25 = 1 remainder 19 |
| 4 | 25 ÷ 19 = 1 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 134 | 11658 |
| 102 and 66 | 1122 |
| 168 and 30 | 840 |
| 76 and 140 | 2660 |
| 99 and 181 | 17919 |