Least Common Multiple (LCM) of 139 and 75
The least common multiple (LCM) of 139 and 75 is 10425.
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 139 and 75?
First, calculate the GCD of 139 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 75 = 1 remainder 64 |
| 2 | 75 ÷ 64 = 1 remainder 11 |
| 3 | 64 ÷ 11 = 5 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 28 | 140 |
| 136 and 37 | 5032 |
| 176 and 84 | 3696 |
| 45 and 12 | 180 |
| 189 and 63 | 189 |