Least Common Multiple (LCM) of 45 and 188
The least common multiple (LCM) of 45 and 188 is 8460.
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 45 and 188?
First, calculate the GCD of 45 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 188 = 0 remainder 45 |
| 2 | 188 ÷ 45 = 4 remainder 8 |
| 3 | 45 ÷ 8 = 5 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 199 | 12935 |
| 162 and 73 | 11826 |
| 41 and 40 | 1640 |
| 129 and 134 | 17286 |
| 37 and 60 | 2220 |