Least Common Multiple (LCM) of 75 and 139
The least common multiple (LCM) of 75 and 139 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 75 and 139?
First, calculate the GCD of 75 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 139 = 0 remainder 75 |
| 2 | 139 ÷ 75 = 1 remainder 64 |
| 3 | 75 ÷ 64 = 1 remainder 11 |
| 4 | 64 ÷ 11 = 5 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 68 | 5644 |
| 181 and 174 | 31494 |
| 138 and 118 | 8142 |
| 23 and 169 | 3887 |
| 173 and 157 | 27161 |