Least Common Multiple (LCM) of 135 and 188
The least common multiple (LCM) of 135 and 188 is 25380.
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 135 and 188?
First, calculate the GCD of 135 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 188 = 0 remainder 135 |
| 2 | 188 ÷ 135 = 1 remainder 53 |
| 3 | 135 ÷ 53 = 2 remainder 29 |
| 4 | 53 ÷ 29 = 1 remainder 24 |
| 5 | 29 ÷ 24 = 1 remainder 5 |
| 6 | 24 ÷ 5 = 4 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 89 | 10502 |
| 64 and 109 | 6976 |
| 147 and 60 | 2940 |
| 44 and 88 | 88 |
| 174 and 130 | 11310 |