Least Common Multiple (LCM) of 75 and 138
The least common multiple (LCM) of 75 and 138 is 3450.
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 75 and 138?
First, calculate the GCD of 75 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 138 = 0 remainder 75 |
| 2 | 138 ÷ 75 = 1 remainder 63 |
| 3 | 75 ÷ 63 = 1 remainder 12 |
| 4 | 63 ÷ 12 = 5 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 193 | 32424 |
| 52 and 159 | 8268 |
| 101 and 152 | 15352 |
| 199 and 138 | 27462 |
| 200 and 12 | 600 |