Least Common Multiple (LCM) of 86 and 119
The least common multiple (LCM) of 86 and 119 is 10234.
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 86 and 119?
First, calculate the GCD of 86 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 119 = 0 remainder 86 |
| 2 | 119 ÷ 86 = 1 remainder 33 |
| 3 | 86 ÷ 33 = 2 remainder 20 |
| 4 | 33 ÷ 20 = 1 remainder 13 |
| 5 | 20 ÷ 13 = 1 remainder 7 |
| 6 | 13 ÷ 7 = 1 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 61 | 5124 |
| 56 and 192 | 1344 |
| 199 and 10 | 1990 |
| 145 and 15 | 435 |
| 156 and 108 | 1404 |