Least Common Multiple (LCM) of 59 and 123
The least common multiple (LCM) of 59 and 123 is 7257.
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 123?
First, calculate the GCD of 59 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 123 = 0 remainder 59 |
| 2 | 123 ÷ 59 = 2 remainder 5 |
| 3 | 59 ÷ 5 = 11 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 149 | 21009 |
| 146 and 145 | 21170 |
| 52 and 36 | 468 |
| 26 and 149 | 3874 |
| 199 and 57 | 11343 |