Least Common Multiple (LCM) of 23 and 58
The least common multiple (LCM) of 23 and 58 is 1334.
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 58?
First, calculate the GCD of 23 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 58 = 0 remainder 23 |
| 2 | 58 ÷ 23 = 2 remainder 12 |
| 3 | 23 ÷ 12 = 1 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 14 | 1092 |
| 127 and 181 | 22987 |
| 122 and 157 | 19154 |
| 26 and 15 | 390 |
| 67 and 74 | 4958 |