Least Common Multiple (LCM) of 188 and 113
The least common multiple (LCM) of 188 and 113 is 21244.
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 113?
First, calculate the GCD of 188 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 113 = 1 remainder 75 |
| 2 | 113 ÷ 75 = 1 remainder 38 |
| 3 | 75 ÷ 38 = 1 remainder 37 |
| 4 | 38 ÷ 37 = 1 remainder 1 |
| 5 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 86 | 5504 |
| 132 and 21 | 924 |
| 12 and 53 | 636 |
| 177 and 33 | 1947 |
| 54 and 156 | 1404 |