Least Common Multiple (LCM) of 150 and 188
The least common multiple (LCM) of 150 and 188 is 14100.
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 150 and 188?
First, calculate the GCD of 150 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 188 = 0 remainder 150 |
| 2 | 188 ÷ 150 = 1 remainder 38 |
| 3 | 150 ÷ 38 = 3 remainder 36 |
| 4 | 38 ÷ 36 = 1 remainder 2 |
| 5 | 36 ÷ 2 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 147 | 27489 |
| 113 and 36 | 4068 |
| 17 and 127 | 2159 |
| 165 and 132 | 660 |
| 15 and 80 | 240 |