Least Common Multiple (LCM) of 186 and 120
The least common multiple (LCM) of 186 and 120 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 186 and 120?
First, calculate the GCD of 186 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 120 = 1 remainder 66 |
| 2 | 120 ÷ 66 = 1 remainder 54 |
| 3 | 66 ÷ 54 = 1 remainder 12 |
| 4 | 54 ÷ 12 = 4 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 75 | 7725 |
| 155 and 120 | 3720 |
| 165 and 15 | 165 |
| 73 and 98 | 7154 |
| 186 and 24 | 744 |