Least Common Multiple (LCM) of 113 and 76
The least common multiple (LCM) of 113 and 76 is 8588.
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 76?
First, calculate the GCD of 113 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 76 = 1 remainder 37 |
| 2 | 76 ÷ 37 = 2 remainder 2 |
| 3 | 37 ÷ 2 = 18 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 15 | 1020 |
| 159 and 132 | 6996 |
| 143 and 136 | 19448 |
| 197 and 10 | 1970 |
| 17 and 122 | 2074 |