Least Common Multiple (LCM) of 59 and 23
The least common multiple (LCM) of 59 and 23 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 59 and 23?
First, calculate the GCD of 59 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 23 = 2 remainder 13 |
| 2 | 23 ÷ 13 = 1 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 11 | 99 |
| 114 and 64 | 3648 |
| 192 and 61 | 11712 |
| 133 and 81 | 10773 |
| 123 and 14 | 1722 |