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 |
|---|---|
| 107 and 69 | 7383 |
| 130 and 57 | 7410 |
| 33 and 194 | 6402 |
| 120 and 119 | 14280 |
| 140 and 100 | 700 |