Least Common Multiple (LCM) of 188 and 42
The least common multiple (LCM) of 188 and 42 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 188 and 42?
First, calculate the GCD of 188 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 42 = 4 remainder 20 |
| 2 | 42 ÷ 20 = 2 remainder 2 |
| 3 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 21 | 336 |
| 112 and 149 | 16688 |
| 165 and 150 | 1650 |
| 17 and 102 | 102 |
| 140 and 30 | 420 |