Least Common Multiple (LCM) of 118 and 123
The least common multiple (LCM) of 118 and 123 is 14514.
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 118 and 123?
First, calculate the GCD of 118 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 123 = 0 remainder 118 |
| 2 | 123 ÷ 118 = 1 remainder 5 |
| 3 | 118 ÷ 5 = 23 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 59 | 8024 |
| 55 and 141 | 7755 |
| 11 and 72 | 792 |
| 149 and 121 | 18029 |
| 128 and 133 | 17024 |