Least Common Multiple (LCM) of 113 and 87
The least common multiple (LCM) of 113 and 87 is 9831.
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 87?
First, calculate the GCD of 113 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 87 = 1 remainder 26 |
| 2 | 87 ÷ 26 = 3 remainder 9 |
| 3 | 26 ÷ 9 = 2 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 134 | 18358 |
| 20 and 146 | 1460 |
| 12 and 99 | 396 |
| 73 and 50 | 3650 |
| 193 and 131 | 25283 |