Least Common Multiple (LCM) of 188 and 116
The least common multiple (LCM) of 188 and 116 is 5452.
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 116?
First, calculate the GCD of 188 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 116 = 1 remainder 72 |
| 2 | 116 ÷ 72 = 1 remainder 44 |
| 3 | 72 ÷ 44 = 1 remainder 28 |
| 4 | 44 ÷ 28 = 1 remainder 16 |
| 5 | 28 ÷ 16 = 1 remainder 12 |
| 6 | 16 ÷ 12 = 1 remainder 4 |
| 7 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 96 | 96 |
| 155 and 149 | 23095 |
| 113 and 169 | 19097 |
| 34 and 25 | 850 |
| 182 and 103 | 18746 |