Least Common Multiple (LCM) of 119 and 186
The least common multiple (LCM) of 119 and 186 is 22134.
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 186?
First, calculate the GCD of 119 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 186 = 0 remainder 119 |
| 2 | 186 ÷ 119 = 1 remainder 67 |
| 3 | 119 ÷ 67 = 1 remainder 52 |
| 4 | 67 ÷ 52 = 1 remainder 15 |
| 5 | 52 ÷ 15 = 3 remainder 7 |
| 6 | 15 ÷ 7 = 2 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 48 | 480 |
| 24 and 48 | 48 |
| 138 and 99 | 4554 |
| 77 and 170 | 13090 |
| 99 and 75 | 2475 |