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 |
|---|---|
| 108 and 115 | 12420 |
| 70 and 70 | 70 |
| 157 and 172 | 27004 |
| 133 and 195 | 25935 |
| 144 and 78 | 1872 |