Least Common Multiple (LCM) of 119 and 86
The least common multiple (LCM) of 119 and 86 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 119 and 86?
First, calculate the GCD of 119 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 86 = 1 remainder 33 |
| 2 | 86 ÷ 33 = 2 remainder 20 |
| 3 | 33 ÷ 20 = 1 remainder 13 |
| 4 | 20 ÷ 13 = 1 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 44 | 220 |
| 52 and 43 | 2236 |
| 47 and 113 | 5311 |
| 32 and 42 | 672 |
| 88 and 30 | 1320 |