Least Common Multiple (LCM) of 40 and 188
The least common multiple (LCM) of 40 and 188 is 1880.
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 40 and 188?
First, calculate the GCD of 40 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 188 = 0 remainder 40 |
| 2 | 188 ÷ 40 = 4 remainder 28 |
| 3 | 40 ÷ 28 = 1 remainder 12 |
| 4 | 28 ÷ 12 = 2 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 72 | 1368 |
| 198 and 39 | 2574 |
| 96 and 35 | 3360 |
| 33 and 107 | 3531 |
| 192 and 132 | 2112 |