Least Common Multiple (LCM) of 120 and 188
The least common multiple (LCM) of 120 and 188 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 120 and 188?
First, calculate the GCD of 120 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 188 = 0 remainder 120 |
| 2 | 188 ÷ 120 = 1 remainder 68 |
| 3 | 120 ÷ 68 = 1 remainder 52 |
| 4 | 68 ÷ 52 = 1 remainder 16 |
| 5 | 52 ÷ 16 = 3 remainder 4 |
| 6 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 59 | 10679 |
| 114 and 21 | 798 |
| 111 and 196 | 21756 |
| 103 and 47 | 4841 |
| 139 and 185 | 25715 |