Least Common Multiple (LCM) of 42 and 188
The least common multiple (LCM) of 42 and 188 is 3948.
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 42 and 188?
First, calculate the GCD of 42 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 188 = 0 remainder 42 |
| 2 | 188 ÷ 42 = 4 remainder 20 |
| 3 | 42 ÷ 20 = 2 remainder 2 |
| 4 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 21 | 3045 |
| 121 and 75 | 9075 |
| 86 and 194 | 8342 |
| 186 and 199 | 37014 |
| 161 and 138 | 966 |