Least Common Multiple (LCM) of 23 and 87
The least common multiple (LCM) of 23 and 87 is 2001.
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 23 and 87?
First, calculate the GCD of 23 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 87 = 0 remainder 23 |
| 2 | 87 ÷ 23 = 3 remainder 18 |
| 3 | 23 ÷ 18 = 1 remainder 5 |
| 4 | 18 ÷ 5 = 3 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 158 | 8848 |
| 176 and 151 | 26576 |
| 77 and 109 | 8393 |
| 183 and 30 | 1830 |
| 191 and 90 | 17190 |