Least Common Multiple (LCM) of 100 and 188
The least common multiple (LCM) of 100 and 188 is 4700.
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 100 and 188?
First, calculate the GCD of 100 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 188 = 0 remainder 100 |
| 2 | 188 ÷ 100 = 1 remainder 88 |
| 3 | 100 ÷ 88 = 1 remainder 12 |
| 4 | 88 ÷ 12 = 7 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 185 | 555 |
| 165 and 93 | 5115 |
| 18 and 54 | 54 |
| 102 and 90 | 1530 |
| 41 and 75 | 3075 |