Least Common Multiple (LCM) of 119 and 123
The least common multiple (LCM) of 119 and 123 is 14637.
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 119 and 123?
First, calculate the GCD of 119 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 123 = 0 remainder 119 |
| 2 | 123 ÷ 119 = 1 remainder 4 |
| 3 | 119 ÷ 4 = 29 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 68 | 12988 |
| 61 and 90 | 5490 |
| 38 and 17 | 646 |
| 97 and 112 | 10864 |
| 186 and 115 | 21390 |