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 |
|---|---|
| 120 and 138 | 2760 |
| 106 and 106 | 106 |
| 128 and 150 | 9600 |
| 51 and 61 | 3111 |
| 103 and 68 | 7004 |