Least Common Multiple (LCM) of 119 and 103
The least common multiple (LCM) of 119 and 103 is 12257.
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 103?
First, calculate the GCD of 119 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 103 = 1 remainder 16 |
| 2 | 103 ÷ 16 = 6 remainder 7 |
| 3 | 16 ÷ 7 = 2 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 170 | 10370 |
| 112 and 88 | 1232 |
| 79 and 140 | 11060 |
| 74 and 40 | 1480 |
| 195 and 61 | 11895 |