Least Common Multiple (LCM) of 138 and 75
The least common multiple (LCM) of 138 and 75 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 138 and 75?
First, calculate the GCD of 138 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 75 = 1 remainder 63 |
| 2 | 75 ÷ 63 = 1 remainder 12 |
| 3 | 63 ÷ 12 = 5 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 76 | 1824 |
| 200 and 187 | 37400 |
| 169 and 71 | 11999 |
| 194 and 116 | 11252 |
| 112 and 89 | 9968 |