Least Common Multiple (LCM) of 34 and 188
The least common multiple (LCM) of 34 and 188 is 3196.
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 34 and 188?
First, calculate the GCD of 34 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 188 = 0 remainder 34 |
| 2 | 188 ÷ 34 = 5 remainder 18 |
| 3 | 34 ÷ 18 = 1 remainder 16 |
| 4 | 18 ÷ 16 = 1 remainder 2 |
| 5 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 129 | 8643 |
| 101 and 100 | 10100 |
| 75 and 32 | 2400 |
| 113 and 140 | 15820 |
| 188 and 59 | 11092 |