Least Common Multiple (LCM) of 120 and 186
The least common multiple (LCM) of 120 and 186 is 3720.
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 120 and 186?
First, calculate the GCD of 120 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 186 = 0 remainder 120 |
| 2 | 186 ÷ 120 = 1 remainder 66 |
| 3 | 120 ÷ 66 = 1 remainder 54 |
| 4 | 66 ÷ 54 = 1 remainder 12 |
| 5 | 54 ÷ 12 = 4 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 24 | 408 |
| 117 and 194 | 22698 |
| 63 and 89 | 5607 |
| 134 and 122 | 8174 |
| 99 and 125 | 12375 |