Least Common Multiple (LCM) of 119 and 130
The least common multiple (LCM) of 119 and 130 is 15470.
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 130?
First, calculate the GCD of 119 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 130 = 0 remainder 119 |
| 2 | 130 ÷ 119 = 1 remainder 11 |
| 3 | 119 ÷ 11 = 10 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 23 | 1541 |
| 165 and 89 | 14685 |
| 196 and 176 | 8624 |
| 86 and 163 | 14018 |
| 122 and 120 | 7320 |