Least Common Multiple (LCM) of 188 and 120
The least common multiple (LCM) of 188 and 120 is 5640.
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 188 and 120?
First, calculate the GCD of 188 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 120 = 1 remainder 68 |
| 2 | 120 ÷ 68 = 1 remainder 52 |
| 3 | 68 ÷ 52 = 1 remainder 16 |
| 4 | 52 ÷ 16 = 3 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 59 | 11033 |
| 67 and 133 | 8911 |
| 115 and 33 | 3795 |
| 32 and 27 | 864 |
| 117 and 153 | 1989 |