Least Common Multiple (LCM) of 123 and 58
The least common multiple (LCM) of 123 and 58 is 7134.
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 123 and 58?
First, calculate the GCD of 123 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 58 = 2 remainder 7 |
| 2 | 58 ÷ 7 = 8 remainder 2 |
| 3 | 7 ÷ 2 = 3 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 111 | 2553 |
| 34 and 21 | 714 |
| 174 and 129 | 7482 |
| 88 and 188 | 4136 |
| 133 and 150 | 19950 |