Least Common Multiple (LCM) of 23 and 59
The least common multiple (LCM) of 23 and 59 is 1357.
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 59?
First, calculate the GCD of 23 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 59 = 0 remainder 23 |
| 2 | 59 ÷ 23 = 2 remainder 13 |
| 3 | 23 ÷ 13 = 1 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 134 | 12328 |
| 100 and 52 | 1300 |
| 186 and 123 | 7626 |
| 93 and 97 | 9021 |
| 122 and 63 | 7686 |