Least Common Multiple (LCM) of 97 and 188
The least common multiple (LCM) of 97 and 188 is 18236.
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 97 and 188?
First, calculate the GCD of 97 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 188 = 0 remainder 97 |
| 2 | 188 ÷ 97 = 1 remainder 91 |
| 3 | 97 ÷ 91 = 1 remainder 6 |
| 4 | 91 ÷ 6 = 15 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 100 | 400 |
| 186 and 91 | 16926 |
| 63 and 142 | 8946 |
| 138 and 152 | 10488 |
| 107 and 123 | 13161 |