Least Common Multiple (LCM) of 120 and 185
The least common multiple (LCM) of 120 and 185 is 4440.
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 185?
First, calculate the GCD of 120 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 185 = 0 remainder 120 |
| 2 | 185 ÷ 120 = 1 remainder 65 |
| 3 | 120 ÷ 65 = 1 remainder 55 |
| 4 | 65 ÷ 55 = 1 remainder 10 |
| 5 | 55 ÷ 10 = 5 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 42 | 714 |
| 100 and 126 | 6300 |
| 129 and 160 | 20640 |
| 104 and 182 | 728 |
| 98 and 28 | 196 |